Austin Texas best lawn weed killer (safe for dogs )

So as many know it is very hard to keep your lawn looking great when you have a dog. I wanted to see if there were any recommendations for how to get rid of weeds for my lawn without harming my dog.
For context I haven’t touched the backyard , only
To mow, but there is just a ton of weeds , it’s like half weed half lawn and I want to get rid of it.
I’ve thought about using round up to get rid of everything and start fresh and just not let my dog out for acouple days in the backyard.
Any recommendations?