Your dd sounds quite a bit like my older dd (age 11 now) right down to the amazing memory & great small motor skills and slower gross motor skills. Mine, however, wasn't reading as early as yours but she really took off once she did. I have a few thoughts.
First, I would personally not move her to the more academic kindergarten. She will already know the material and probably be frustrated with the stress on academics she has already mastered.
In our area, too, we have a lot of kids who are held out for K and are quite a bit older as a result. Both of my girls have late summer/fall bds and are much younger. I don't regret starting them when I did even if their grade peers are sometimes 18 months+ older than they are. Dd#1 wound up skipping 5th grade, so she is 2-2.5 yrs younger than some of the kids in her grade at this point. Although some are still just a year or so older.
We are moving more in the direction of homeschooling at this point. Dd#2 is supplementing at home/partially hsing and we are researching hsing for the year after next when they hit middle school and high school respectively. This is, of course, not the only route and may not be the one for your family or dd.
The worst year dd#1 had in school was first grade. This is the reason I'm advising not going toward the schooling with a greater emphasis on academics. Dd#1's first grade was a pressure cooker with flash cards for sight words & math facts, timed tests for math facts, and copious amounts of repetition in the form of repeated readings of the same books to gain fluency, writing spelling words over and over and in sentences to memorize them, etc. She totally fell apart, worked very slowly, missed recess to complete work, and started telling me that she wished she had never been born.
She knew the material but was too young at 6 to cope with being drilled over and over on things she already knew. I doubt that a more academic focused K program is going to be academically appropriate for the degree of advancement that you describe. It is probably just going to be a higher pressured environment with more testing, more focus on learning the fundamentals and getting many of the kids above grade level (but still less ahead than your dd already is).
I'd stick with the play based program for pre-K and K and then reevaluate in 1st. At that point, your best bets are probably going to be a more academic program with significant subject acceleration (sending her to a higher grade classroom for certain subjects including language arts), homeschooling, skipping a grade, or a self contained gifted program that isn't just a high achiever program but a program designed for kids who learn differently.
