I am going to advise you coming from a mom that had to make the same decision years ago to keep her in Pre K. She won't even be five until mid year Kindergarten, which I am surprised they would allow her as our public school system has a cut off of end of Septemeber here.
Here is my story- My daughter turned 5 first week of September, because she was doing so well academically in Pre K I put her in as I wanted to challenge her. She is almost the youngest in her class and has been every year.
Most of her friends are now 8 or will be in the next month. She is now 7 and in second grade, going into 3rd. She will be into third grade for three weeks before she turns 8.
Over the years I have seen her shine academically, she is above in reading levels. She was right where your daughter was, could write her name, know her address, phone number, all her colors, shapes, letters, numbers...but the maturity was so not there and for girls I think that is so hard on them in each grade level. I have seen my daughter struggle with friendships on occassions and focusing in class.
With her lack of maturity she has had problems focusing, peer issues, talking too much in class, not listening or following instructions and things that come along with being more mature. All her teachers EVERY single year remind me when she is having a problem that it has much more to do with her age and she will eventually catch up. All her teacher praise how smart she is but they each one have brought up the maturity thing. I felt so awful after they would remind me how young in mind she is still!!! :)
I now wish I had waited, there was no reason to rush her into Kindergarten and I made a mistake. She has grown up a lot this year and her second grade teacher said mid year third grade she thinks the light bulb will kick on maturity wise.
I could have saved her a lot of grief if I had just waited. I would NEVER at this point consider holding her back with the friends she has made and how humliating at this point it would be for her, however if you could wind the clock back I wouldn't have put her in so young. Girls mature faster in a sense that a lot of the girls in her grade are older and more mature then she is. She is very emotionally driven and that can cause problems at times.
My son who will be five in July, I just had to do this again. I sat with his Pre K teachers for hours trying to make sure I was making the right choice for him as well. Thankfully, he is right where boys his age should be and will be on a more even playing field. So he will start Kindergarten in the fall.