It probably is a good idea to research what your local school district offers for gifted children. That can help you decide how to address the September birthday.
To give you a few anecdotal examples...
My DD is in second grade. In our district, a once-a-week gifted pull-out program is available starting in second grade and a full-time gifted class is available starting in third grade.
One of the boys in my DD's gifted class has been in the same class since kindergarten and his birthday is the first week of September. I would also guess that this classmate is highly gifted.
My DD is moderately gifted with an April birthday.
In school, DD has had a great experience. We used preschool as a means of letting her build social skills and learn how school "works" -- things like sitting quietly during circle time, lining up, etc. We didn't worry about the academic piece of it and just continued sort of a simultaneous "homeschool" preschool to address her thirst for learning. Now that she is in public school, the gifted program is a good fit. Without having the full-time accelerated gifted program in place, I would not be nearly so satisfied.
In contrast, my DD's slightly-older and more gifted(?) classmate has had a few more issues. School has been good for him socially, but he has been SOOOOO bored. For example, earlier this year, he successfully executed a plan to "escape" from school with a classmate, go to a park, collect money from home, and head off to a restaurant. The boys were eventually found a few hours after the big escape, after causing much panic among many adults.
For him, the wait until the full-time gifted program kicks in has probably been too long. They are now putting him in a third grade class each day for math (sort of accelerating him early). With 20/20 hindsight, he probably would have been better served if he had started school a year earlier. It isn't advertised, but I gather that skipping kindergarten IS possible in our state, despite the standard cut-off. Even if that wasn't possible, the school could have started accelerating him into higher grade math and/or reading as early as kindegarten, which may have averted some of the problems.
