My birth state requires surgery to change the birth certificate. The surgery is non-specific, so just top surgery should do it. But for the Georgia driver license, it's the same thing - surgeon's letter:
1. Gender updates requires applicant to submit a court order or physician's letter certifying gender change.
2. The letter or court order shall state the person's name, date of birth, date of gender reassignment operation and other identifying information.
I find #2 to be rather vague, and as such, I think a well worded vague letter from the surgeon will suffice.