You will have to talk to someone in your school district to find out the answer, or talk to an educational consultant about it. You can get contact information from the education.com SchoolFinder application (URL below) by entering your zip code, click Search, then choose the elementary school near you for contact info. Or just Google search your school district to find their web page.
There may be better alternatives for your child that would be more enriching than public school kindergarten. I don't know what is available in your area - we have something called "Challenger School" which, at least when my kids were that age, provided a good environment for bright kids.
And waiting a year to put your child in kindergarten isn't setting him or her back at all. In some cases it's a good thing because your child may be better prepared emotionally for school.
Typically school systems are pretty strict about not letting kids who miss the deadline into public Kindergarten. Many private schools have later deadlines (so a child with a late September birthday may be eligible for private Kindergarten but not public). But it may not be as easy as doing K in private school and then switching to public for first grade. The public school may make the student repeat Kindergarten.
As Bob suggested, calling your school district office to discuss options is probably the best thing to do.