It will be highly doubtful, but you maybe near a school where they will entertain the idea. Chances are your child will need to demonstrate that she is ready and capable.
My wife and nephew missed the cut off as well by a few days, but the school system doesnt consider any other factors. My nephew has had a difficult time with this as his cousin was born two weeks before him yet he is in a higher grade, and my son is 8 months younger than him but is in the same grade as him.
It is extremely difficult in public schools. In my state (Oregon) kindergarten is considered optional. I know a lot of parents that enter their child into a private kindergarten then transfer them into first grade at a public school. A lot of preschools offer kindergarten as well. It may take a little research but it can be well worth it in the long run.
If you would prefer her to go straight to public school, talk to the local school board, principal, and enrollment offices. If your daughter knows her ABC's, is counting to 10, can communicate, and is potty trained some schools will make an exception.
The key is going to be a lot of leg work, and research on your part.
Public schools will not let you start early, no exception. Some private schools may let her start early depending on her abilities. But most places have a cut of date in place and will not change it. If they let you in then they have to let everyone in. My daughter's birthday is on the 8th, so I feel your pain! Some states in the north east have December cut offs.