Jorah Mormont's "Report from Qarth" (Spoilers Extended)

Background

"I did, Your Grace." The old knight took pains not to look at her bare breast as he spoke to her.

Ser Jorah would not turn his eyes away. He loved me as a woman, where Ser Barristan loves me only as his queen. Mormont had been an informer, reporting to her enemies in Westeros, yet he had given her good counsel too. "What do you think of it? Of him?" -ADWD, Daenerys III

In this post I thought it would be interesting to discuss the spying that Jorah Mormont was doing on Daenerys back in the first few books (before she exiled him), with a primary focus on the report he made from Qarth.

If interested: Jorah Mormont: The Demon of Slaver's Bay

From very early on in the series, the reader knows that Jorah is informing on Daenerys:

"Do you remember Ser Jorah Mormont?"
"Would that I might forget him," Ned said bluntly. The Mormonts of Bear Island were an old house, proud and honorable, but their lands were cold and distant and poor. Ser Jorah had tried to swell the family coffers by selling some poachers to a Tyroshi slaver. As the Mormonts were bannermen to the Starks, his crime had dishonored the north. Ned had made the long journey west to Bear Island, only to find when he arrived that Jorah had taken ship beyond the reach of Ice and the king's justice. Five years had passed since then.
"Ser Jorah is now in Pentos, anxious to earn a royal pardon that would allow him to return from exile," Robert explained. "Lord Varys makes good use of him." -AGOT, Eddard II

so it makes sense that after the Arstan/Barristan reveal that after sitting on Robert's Small Council (Fools/Flatterers) that Barristan would reveal what Mormont had been up to:

“It may be that I must die a traitor’s death,” Ser Barristan said. “If so, I should not die alone. Before I took Robert’s pardon I fought against him on the Trident. You were on the other side of that battle, Mormont, were you not?” He did not wait for an answer. “Your Grace, I am sorry I misled you. It was the only way to keep the Lannisters from learning that I had joined you. You are watched, as your brother was. Lord Varys reported every move Viserys made, for years. Whilst I sat on the small council, I heard a hundred such reports. And since the day you wed Khal Drogo, there has been an informer by your side selling your secrets, trading whispers to the Spider for gold and promises.”
He cannot mean … “You are mistaken.” Dany looked at Jorah Mormont. “Tell him he’s mistaken. There’s no informer. Ser Jorah, tell him. We crossed the Dothraki sea together, and the red waste …” Her heart fluttered like a bird in a trap. “Tell him, Jorah. Tell him how he got it wrong.” -ASOS, Daenerys V

and Jorah mentions that he stopped reporting in Qarth:

“You warned me against everyone except yourself.” His insolence angered her. He should be humbler. He should beg for my forgiveness. “Trust no one but Jorah Mormont, you said … and all the time you were the Spider’s creature!”
“I am no man’s creature. I took the eunuch’s gold, yes. I learned some ciphers and wrote some letters, but that was all—”
“All? You spied on me and sold me to my enemies!”
“For a time.” He said it grudgingly. “I stopped.”
“When? When did you stop?”
“I made one report from Qarth, but—”
“From Qarth?” Dany had been hoping it had ended much earlier. -ASOS, Daenerys VI

so I thought it would be interesting to take a look at the primary information that Jorah shared:

• Daenerys' Marriage to Drogo

“So the slaver has become a spy,” Ned said with distaste. He handed the letter back. “I would rather he become a corpse.”
“Varys tells me that spies are more useful than corpses,” Robert said. “Jorah aside, what do you make of his report?”
“Daenerys Targaryen has wed some Dothraki horse-lord. What of it? Shall we send her a wedding gift?” -AGOT, Eddard II

• Daenerys' Pregnancy

Jorah also shared that Dany was pregnant:

Ned looked at the eunuch coldly. “You would bring us the whisperings of a traitor half a world away, my lord. Perhaps Mormont is wrong. Perhaps he is lying.”
“Ser Jorah would not dare deceive me,” Varys said with a sly smile. “Rely on it, my lord. The princess is with child.”
...
Robert turned to face his Hand. “Well, there it is, Ned. You and Selmy stand alone on this matter. The only question that remains is, who can we find to kill her?”
“Mormont craves a royal pardon,” Lord Renly reminded them.
“Desperately,” Varys said, “yet he craves life even more. By now, the princess nears Vaes Dothrak, where it is death to draw a blade. If I told you what the Dothraki would do to the poor man who used one on a khaleesi, none of you would sleep tonight.” He stroked a powdered cheek. “Now, poison … the tears of Lys, let us say. Khal Drogo need never know it was not a natural death.”-AGOT, Eddard VIII

and:

“When? When did you stop?”
“I made one report from Qarth, but—”
“From Qarth?” Dany had been hoping it had ended much earlier. “What did you write from Qarth? That you were my man now, that you wanted no more of their schemes?” Ser Jorah could not meet her eyes. “When Khal Drogo died, you asked me to go with you to Yi Ti and the Jade Sea. Was that your wish or Robert’s?”
“That was to protect you,” he insisted. “To keep you away from them. I knew what snakes they were …”
“Snakes? And what are you, ser?” Something unspeakable occurred to her. “You told them I was carrying Drogo’s child …”
“Khaleesi …”
“Do not think to deny it, ser,” Ser Barristan said sharply. “I was there when the eunuch told the council, and Robert decreed that Her Grace and her child must die. You were the source, ser. There was even talk that you might do the deed, for a pardon.”
“A lie.” Ser Jorah’s face darkened. “I would never … Daenerys, it was me who stopped you from drinking the wine.”
“Yes. And how was it you knew the wine was poisoned?”
“I … I but suspected … the caravan brought a letter from Varys, he warned me there would be attempts. He wanted you watched, yes, but not harmed.” He went to his knees. “If I had not told them someone else would have. You know that.”
-ASOS, Daenerys VI

resulting in attempts on her/her child's life:

"Have to?" It was too late. He should have begun by begging forgiveness. She could not pardon him as she'd intended. She had dragged the wineseller behind her horse until there was nothing left of him. Didn't the man who brought him deserve the same? This is Jorah, my fierce bear, the right arm that never failed me. I would be dead without him, but . . . "I can't forgive you," she said. "I can't." -ASOS, Daenerys VI

• Birth of Dragons

While not confirmed, Jorah also likely told Varys about the birth of Daenerys' dragons if we remember that he made a report from Qarth, by the time Jorah's report reached Westeros, time had likely passed. Obviously Varys didn't want to let that be known, so would have reported it in an inconspicuous manner:

The eunuch drew a parchment from his sleeve. “A kraken has been seen off the Fingers.” He giggled. “Not a Greyjoy, mind you, a true kraken. It attacked an Ibbenese whaler and pulled it under. There is fighting on the Stepstones, and a new war between Tyrosh and Lys seems likely. Both hope to win Myr as ally. Sailors back from the Jade Sea report that a three-headed dragon has hatched in Qarth, and is the wonder of that city—”
“Dragons and krakens do not interest me, regardless of the number of their heads,” said Lord Tywin. “Have your whisperers perchance found some trace of my brother’s son?” -ASOS, Tyrion III

If interested: Dragon Rumors

TLDR: While reporting back to Varys on Daenerys, Jorah Mormont told about Dany's marriage and pregnancy. These were known by the Small Council prior to Dany/Jorah arriving in Qarth. From looking at what valuable information Jorah could have shared with Varys while he was in Qarth, it is likely he mentioned the hatching of Dany's three dragons.