Homeschool and don't look back!
I can give you advice (I hope) from your daughter's perspective, though not from the parental perspective, but first I want to address the issue of social opportunities.
First of all, I have become convinced that school is a pretty terrible place to learn social skills, and it's even more so for kids who are fairly outside the norm in some way or another. (More on that later from my own experience)
Secondly, from what I have seen of LDS churches, there should be plenty of opportunity for social activity there. They're pretty active churches, it seems to me. You can also join a support group that meets regularly.
Ok, on to my experience in school. I was also brighter than average, and advanced for my age. I learned how to read at four, though I don't know if I was doing second-grade reading and math. Kindergarten was ok for me, because it was mostly playtime, but 1st grade suddenly became excruciatingly boring. I checked out mentally. Fortunately my parents put me in an accelerated private school, and taught me things at home, and I am eternally grateful that they did both of those things. I have often wished they would have just homeschooled me. I would have learned more, wasted less time going over stuff I had known for years, and it would have been better socially as well. I was shy, and I did better in a situation with fewer people around that I could get to know well (the private school was smaller than the public one), and I think I would have done even better if I were homeschooled.