My DS5 tested very similar to your DD but his birthday is at the end of August, so starting K worked ok for him. I like the idea of asking for your DD to enter K now, because they do need to learn about school, but it won't take long for her to learn the routine and then boredom begins. She will be so ready for 1st grade, maybe even 2nd by the time September rolls around.
In hindsight, we were very lucky because our DS's preschool teacher arranged a conference over the summer at our local public school with the principal, herself and me. We brought all our "professional" reports, and his former teacher led the meeting and basically told them, "challenge this kid or he will find something else to do and it probably won't be good."
Because this came from someone other than me, they really took it to heart. His teacher has tried to challenge him from the start and she immediately recognized his abilities. Next week he will begin the math EPGY in her classroom during their math time. This was her idea not mine, although we are paying for it.
One thing my son is completely average in is writing. He reads way above peers, his math is great, but his writing is just plain average. It is not uncommon to find this in gifted kids apparently. Because of this, I think Kindergarten has been good for him but I don't know what we will do with him next year.
A lot will depend on the teacher. If you have an advocate that could meet with you and the school, like a previous teacher or psychologist, I think that goes a long way. Then it's not just you sitting there saying, "hey, look at my kid!". Good luck.
