Only an occasional viewer/poster by now. Gifted kids ARE different. They will always be the round/square peg in the opposite hole for many things.
Our son with a fall birthday went early for kindergarten (age 4 at start), was with first graders in spring and reading at a 4th or 5th grade level. Not ready for straight second grade and was in a 1-3 mixed class, a 3-4 class and skipped 4th grade. He started at flagship U while still 16.
He was with the same cohort for 5th through HS so he had the same experiences as those he started college with. An introvert, he had like minded HS friends. Like parents, socially not gifted.
I looked at gap year possibilities but before age 18 there are so many limitations for travel and such for minors. He needed intellectual stimulation so college work at a top tier school to be with peers was needed. Working or doing things independently would not have been a good choice.
My biggest worry in sending him off to big U was whether he would get up in time for classes. This was the kid whose loud alarm we heard down the hall but he was oblivious to. He did not have any problems- he was motivated to attend. The legal drinking age is 21 (unlike my college years) so he was not different than other college freshmen (you can tell your kid does not have a virgin liver when they easily handle a holiday wine at home).
He had several Honors classes- he wasn’t even the youngest in his freshman honors physics as there was a 14 year old girl doing WI Youth Options in the class. He ended up with an honors math major and added computer science (doing a 5th year) when he over reached for elite grad schools (math is extremely competitive, he was not the top student at his top 20 U). He ended up working, recruited eventually by a top company. He likes development more than research and CS advanced degrees are not useful. He self teaches anything he needs. We were disappointed he did not choose to go further- MS and/or PhD but he is still just as smart and well read et al.
OP- going on to a top tier college where your D can be with intellectual peers is likely the best bet. Colleges don’t care (or often know) a student’s age. No the HS social environment. Being among like minded students and finally among intellectual peers is wonderful.
Yes, there will be social issues as there always have been because she is different than the typical college student. Public flagships are two tiered- the usual and the gifted that populate honors programs/colleges.
Let her go for it- never hold her back to be with age mates.