My daughter has an end of September birthday, though NYC has a 12/31 cut-off. Private schools are 9/1, so in the playground she will be one of the younger ones in her grade cohort.
One thing, she prefers older kids to play with and rarely plays with a younger child. To me, that is a big indicator she is ready to be younger in kindergarten.
Although she is slightly smaller for her age cohort, she is very active and takes ballet and gymnastics. I think being very physical and strong in the body helps them with older kids, because they will imitate in the playground and you want your child to be safe and to participate.
Ren
