Background

Since it is such a recurring theme in the D&E novellas, I thought it would be fun to take a look at the different times that Dunk has fought a 1v1 and look at the surrounding incident, etc. in their entirety (at least of the given information) and see how that could potentially project forward.

If interested: Body Count: Named Characters Killed by Individuals in Combat

Note: Dunk crosses swords (and not in the way John the Fiddler meant) with other characters at points in battles such as when the Ironborn attack them while aboard the White Lady but I wouldn't consider it a 1v1 at any point really.

Confirmed

Aerion Brightflame (Puppeteers)

• Primary Mention: The Hedge Knight
• Year: 209AC
• Result: Injuries for Aerion/Dunk Arrested

After Aerion attacks Tanselle, Dunk defends her:

Finally they shoved him down and pinned his arms and legs. Aerion was on his feet again. The prince's mouth was bloody. He pushed inside it with a finger. "You've loosened one of my teeth," he complained, -The Hedge Knight

If interested: The Original Cloth Dragon: The Sons of the Bright Prince

• Primary Mention: The Sworn Sword
• Year: 210/211AC
• Result: Dunk stabs/drowns Lucas

On behalf of Ser Eustace, Dunk fights the Longinch (who desires to marry Rohanne):

Dunk dived forward. Ser Lucas had wrenched his sword free for another cut. Dunk slammed into him waist-high and knocked him off his feet. The stream swallowed both of them again, but this time Dunk was ready. He kept one arm around the Longinch and forced him to the bottom. Bubbles came streaming out from behind Inchfield's battered, twisted visor, but still he fought. He found a rock at the bottom of the stream and began hammering at Dunk's head and hands. Dunk fumbled at his swordbelt. Have I lost the dagger too? he wondered. No, there it was. His hand closed around the hilt and he wrenched it free, and drove it slowly through the churning water, through the iron rings and boiled leather beneath the arm of Lucas the Longinch, turning it as he pushed. Ser Lucas jerked and twisted, and the strength left him. Dunk shoved away and floated. His chest was on fire. A fish flashed past his face, long and white and slender. What's that? he wondered. What's that? What's that? -The Sworn Sword

If interested: Rohanne Webber and her Husbands & Gerold "the Golden" Lannister

Alyn Cockshaw

• Primary Mention: The Mystery Knight
• Year: 212AC
• Result: Dunk pushes Alyn into a well to drown

After Alyn gets jealous of the attention Daemon II is giving Dunk, he lures Dunk to a well intending to kill him.

Dunk closed his hand around the loose stone. It proved to be less loose than he had hoped. Before he could wrench it free, Ser Alyn lunged. Dunk twisted sideways, so the point of the blade sliced through the meat of his shield arm. And then the stone popped free. Dunk fed it to His Lordship and felt his teeth crack beneath the blow. "The well, is it?" He hit the lordling in the mouth again, then dropped the stone, seized Cockshaw by the wrist, and twisted until a bone snapped and the dagger clattered to the stones. "After you, m'lord." Sidestepping, Dunk yanked at the lordling's arm and planted a kick in the small of his back. Lord Alyn toppled headlong into the well. There was a splash. -The Mystery Knight

Bloodraven/Ser Maynard finds it hilarious:

"Well done, ser."
Dunk whirled. Through the rain, all he could make out was a hooded shape and a single pale white eye. It was only when the man came forward that the shadowed face beneath the cowl took on the familiar features of Ser Maynard Plumm, the pale eye no more than the moonstone brooch that pinned his cloak at the shoulder. -The Mystery Knight

If interested: Bloodraven's Humor in D&E & A great little piece of writing in the series (imo) comes from D&E...

Tommard Heddle

• Primary Mention: The Mystery Knight
• Year: 212AC
• Result: Dunk kills Tommard with a blade to the throat

"You are no knight," said Black Tom. "Are those tears in your eyes, oaf?" Teals of pain. Dunk pushed up off his knee and slammed shield-first into his foe. Black Tom stumbled backwards, yet somehow kept his balance. Dunk bulled right after him, smashing him with the shield again and again, using his size and strength to knock Heddle halfway across the sept. Then he swung the shield aside and slashed out with his longsword, and Heddle screamed as the steel bit through wool and muscle deep into his thigh. His own sword swung wildly, but the blow was desperate and clumsy. Dunk let his shield take it one more time and put all his weight into his answer.

Black Tom reeled back a step and stared down in horror at his forearm flopping on the floor beneath the Stranger's altar. "You," he gasped, "you, you…"

"I told you." Dunk stabbed him through the throat. "I'm better with a sword." -The Mystery Knight

If interested: List of Blackfyre Supporters in each Rebellion

King Daemon III Blackfyre

• Primary Mention: The World of Ice and Fire
• Year: 236AC
• Result: Dunk slays Daemon III

An instance we might get a D&E about but in the Fourth Blackfyre Rebellion, Dunk slays King Daemon III:

The invaders landed on Massey's Hook, south of Blackwater Bay, but few rallied to their banners. King Aegon V himself rode out to meet them, with his three sons by his side. In the Battle of Wendwater Bridge, the Blackfyres suffered a shattering defeat, and Daemon III was slain by the Kingsguard knight Ser Duncan the Tall, the hedge knight for whom "Egg" had served as a squire. -TWOIAF, The Targaryen Kings: Aegon V

If interested: Daemon III Blackfyre

Lyonel Baratheon aka The Laughing Storm

• Primary Mention: The World of Ice and Fire
• Year: 239AC
• Result: Dunk defeats (but seemingly does not kill) Lord Lyonel

While this will likely be the subject of a D&E, our current best source of info on this comes from TWOIAF:

The love between Jenny of Oldstones ("with flowers in her hair") and Duncan, Prince of Dragonflies, is beloved of singers, storytellers, and young maids even to this day, but it caused great grief to Lord Lyonel's daughter and brought shame and dishonor to House Baratheon. So great was the wroth of the Laughing Storm that he swore a bloody oath of vengeance, renounced allegiance to the Iron Throne, and had himself crowned as a new Storm King. Peace was restored only after the Kingsguard knight Ser Duncan the Tall faced Lord Lyonel in a trial by battle, Prince Duncan renounced his claim to crown and throne, and King Aegon V agreed that his youngest daughter, the Princess Rhaelle, would wed Lord Lyonel's heir. -TWOIAF, The Stormlands: House Baratheon

and:

Even that could not restore the peace, nor win back the friendship of Storm's End, however. The father of the spurned girl, Lord Lyonel Baratheon of Storm's End—known as the Laughing Storm and famed for his prowess in battle—was not a man easily appeased when his pride was wounded. A short, bloody rebellion ensued, ending only when Ser Duncan of the Kingsguard defeated Lord Lyonel in single combat, and King Aegon gave his solemn word that his youngest daughter, Rhaelle, would wed Lord Lyonel's heir. To seal the bargain, Princess Rhaelle was sent to Storm's End to serve as Lord Lyonel's cupbearer and companion to his lady wife. 

If interested: Speculating on Dunk & Egg: "The Champion"

Possible

Otho Bracken aka The Brute of Bracken

Otho will likely appear in the "Village Hero" in the D&E series. Although it remains to be seen if he is as his name appears or if it is more of a Rohanne Webber situation, but if the novellas continue the script of Dunk fighting someone, we have him as a potential option.

If interested: Dunk & Egg: "The Village Hero"

Erik Ironmaker/Dagon Greyjoy

Not canon, but only mentioning since the show has an image of Dunk's page in the white book that references rescuing a Lannister from Pyke:

Rescued daughter of Lord Damon Lannister from Pyke after her ship was taken by Greyjoy raiders-GOT WhiteBook screenshot.jpg - A Wiki of Ice and Fire (westeros.org)

If interested: Asha's Husband, the Iron Islands and a Blood Oath

Bonus

I decided to add a few things that weren't necessarily 1v1 since I was on a roll:

Winterfell Melee?

Worth noting that Dunk really isn't a tourney knight and is much better for melees (which I hope to see in an upcoming Dunk and Egg, I am thinking maybe She Wolves since it is in the North):

If there was a melee, I might enter that." Dunk's size and strength would serve him better in a melee than in the lists. -The Mystery Knight

and:

"I am better with a sword than with a lance," he admitted, "and even better with a battleaxe. Will there be a melee here?" His size and strength would stand him in good stead in a melee, and he knew he could give as good as he got. Jousting was another matter. - The Mystery Knight

If interested: What We Know: The She Wolves of Winterfell

Aerion Brightflame (Trial of Seven)

• Primary Mention: The Hedge Knight
• Year: 209AC
• Result: Aerion Brightflame yields/withdraws his accusation

Prince Aerion made a sudden dive for his morningstar. Dunk kicked him in the back and knocked him facedown, then grabbed hold of one of his legs and dragged him across the field. By the time he reached the viewing stand where Lord Ashford sat, the Bright Prince was brown as a privy**. Dunk hauled him onto his feet and rattled him, shaking some of the mud onto Lord Ashford and the fair maid. "Tell him!"**

Aerion Brightflame spit out a mouthful of grass and dirt. "I withdraw my accusation." -The Mystery Knight

If interested: Aerion Brightflame: Connecting the Dots

Uthor Underleaf (Tourney)

• Primary Mention: The Mystery Knight
• Year: 212AC
• Result: Unhorses Dunk with a blow to the head

Uthor is a professional tourney fighter. He easily defeats Dunk:

When ten yards remained between them, Ser Uthor shifted the point of his lance upward. A crack rang in Dunk's ears as his lance hit. He felt the impact in his arm and shoulder, but never saw the blow strike home. Uthor's iron fist took him square between his eyes, with all the force of man and horse behind it.

Dunk woke upon his back, staring up at the arches of a barrel-vaulted ceiling. -The Mystery Knight

If interested: Something Sad I Just Noticed about Dunk/Ser Uthor

Barristan Selmy (Tourney)

• Primary Mention: A Storm of Swords
• Year: 252/253AC
• Result: Defeated by a Mystery Knight (a young Barristan Selmy)

This is from Barristan's entry in the White Book:

Ser Barristan of House Selmy. Firstborn son of Ser Lyonel Selmy of Harvest Hall. Served as squire to Ser Manfred Swann. Named "the Bold" in his 10th year, when he donned borrowed armor to appear as a mystery knight in the tourney at Blackhaven, where he was defeated and unmasked by Duncan, Prince of Dragonflies. Knighted in his 16th year by King Aegon V Targaryen, after performing great feats of prowess as a mystery knight in the winter tourney at King's Landing, defeating Prince Duncan the Small and Ser Duncan the Tall, Lord Commander of the Kingsguard. Slew Maelys the Monstrous, last of the Blackfyre Pretenders, in single combat during the War of the Ninepenny Kings. -ASOS, Jaime VIII

If interested: Mystery Knights in ASOIAF

TLDR: Just a list of named characters that Dunk is confirmed to fight in a 1v1 and then some possible ones that could occur as well.