This isn't as late as you're considering, but my dd13 skipped the last year of elementary (5th) to start middle school a year early. She, too, has a late bd so she was still 9 when she started 6th (although she turned 10 in the early fall). My younger dd is very, very small (like maybe 5th percentile), but my one who skipped is more typical in height.
There was a big step up in terms of the quantity of work going into middle school but I also think that some of that was due to her having gotten into poor study habits due to too much time spend tutoring other students and writing papers the morning they were due and still getting A+s.
The jump in work quantity wasn't too much, though, and she still got straight As throughout middle school and was still in the GT/accelerated classes. I generally think that kids for whom a skip is obvious are so far ahead that they are still top students post-skip. My dd isn't a fast worker either.
It seemed to me that math was the one area where there were the some gaps from skipping that year of math. Again, she still had As in math classes throughout middle school, but she skipped 5th grade math not Algebra. If the skip had occured later and she had tried to skip a higher level math course, I expect that she would have had more catch up there. Math is also my dd's weakest subject.
If your dd is that far ahead in math, I suspect that it wouldn't be a big issue for her unless she isn't a strong writer. Good writing skills are very beneficial to have in place in middle and high school and I think that teachers expect to teach less of how to write a research paper, narrative essay, etc. at that point. If she feels strong in reading, writing, and math, I wouldn't be overly concerned about skipping.
FWIW, introducing my dd to middle schoolers at an early age didn't create a social problem. She wasn't influenced by the kids who were doing things I don't want her involved with. She mostly hung out with other high achieving kids who toed the line.
