S.G.
I am going thru this sitution right now, as my daughter's birthday is in October. She has been attending the full day kindergarten at Chesterbrook in Lisle. It's a great program. We are in the process of applying for early admittance to our Downers Grove grade school.
Let me tell you first off that people are VERY opinionated about this issue. The people that don't believe in early in admittance will be very outspoken to tell you that you are wrong to try to push your child ahead and how bad it will be for them, etc. Don't take it personally. Everyone is entitled to their own opinion. But keep in mind that YOU know your child best, not them. You know if your child is ready, socially and intellectually. If you think she is ready and are willing to go thru the process, then do it.
Even if they are in an accredited kindergarten program, the public school is not required to let them in to 1st grade. If they have gone to kindergarten AND first grade, the public school is required to let them into 2nd grade.
The process (at least in Downers Grove) is:
1) write a letter to the principal at your school with your intention to apply for early admittance
2) schedule a half day session where your child will attend the current 1st grade class, where they will be observed by the teacher, the principal, the school psycholigist, reading specialist, etc. This is to see how they relate and if they are socially ready
3) Do private testing, at your expense. This is to judge intellectual and motor skill readiness. There are 3 areas they are tested in. 2 of these, the child needs to score in the 93rd percentile. Your school should give you a list of names of acceptable people to administer the tests. So, not only does your child have to be at the same level as the other children entering 1st grade, they have to score better than 93% of them!
It really is an individual decision. All children cannot be lumped into a category based on their birth date. Obviously, the public schools need to have a cut off day for the typical child. There are some children who aren't ready yet, and a parent may choose to hold them back. But, there are also the children who are ready early, and it is perfectly acceptable to apply for early admittance.
Good luck! I know I'm hoping for the best in our situation.