Hi , My DD6 was about at the same level as yours when she started kindergarten last fall. She went to full day kinder though, since we don't have a 1/2 day option.
We talked to the teacher before school started, and brought specific examples of what she was reading (and understanding) as well as what math concepts she already knew. With in 2 weeks of school starting she was going to 1st grade for reading, and by Thanksgiving she was going up for math as well. Neither of these were actually challenging for her, but she was very unhappy in kinder because it was so slow and didn't require her to "use her brain" at all (her words)
Once she was going up for those two classes she became much happier and eventually she was moved fulltime into 1st grade.
Her kindergarten teacher really appreciated the heads up, because she had "never had a student like her before..." (boy did I get sick of hearing that phrase) and didn't really know what to do with her. I think the teacher was a bit intimidated because while DD would never complain or act out or even tell her the work was too easy, DD often made suggestions about more things they could do with the work they were being given to make it more interesting. The teacher often asked for our suggestions about what to do with DD because she had no idea what to do. Luckily, the 1st grade teacher "got her" and understood her little quirks and enjoyed having her in class.
So, I guess my advice would be to definitely give the teacher a heads up. Be as specific as possible about her strengths and weaknesses, and her personality. Also ask if there is any option of her doing reading with 1st grade after she gets familiar with how school works. At least then she wouldn't be stuck sitting there listening to kids guess about what sounds which letters make, or how to recognize a G and a g from a random list of letters. (Where we are they only have to count to 32 when they leave!)
Good luck
