If you homeschool, you can work at your DD's pace, interests, needs, etc. It might be the least-worst scenario. Of course, if you can find another school that could work, then perhaps this is a moot point.
By all means you could try a public or private school and see what happens, but I'd be prepared to withdraw DD if it doesn't work out. I didn't set out to homeschool and there are days when I want to pull my hair out, but so far it's been working out and a better solution than any formal school at the moment. I'm trying to take things one day at a time and see the homeschooling as a long-term temporary situation that may change eventually with time. There are more opportunities, for instance, high school+ level, especially online, that possibly opens more doors.
My eg/pg DS7 was in two private gifted schools for pre-k and k; I'm homeschooling him today because neither school could accommodate/accelerate him. At the first school, he rapidly accelerated through the pre-k/k/1st grade curriculum within 2 1/2 months and the headmaster refused to bump him up to the 2nd/3rd grade class even for math, which he was his strong suit. The second school was a bit better in being less structured and classroom-driven, but DS7 still faced issues with not going ahead in math because he hadn't mastered his addition facts properly yet, which was ridiculous to me. He was in kindergarten. Of course, the cost for these private schools became a reason for homeschooling. At least with homeschooling this year, I've got a much better grasp on what DS7's cognitive abilities are rather than relying on what little his former teachers said.
There's a lot of variables with schools from the teachers to the curriculum to the other students that most neurotypical parents don't have to face. Between NCLB and the emphasis on standards, most teachers devote their energies to the ones struggling in class and to learn rather than the ones who have already mastered the material or are bored due to the lack of academic opportunities. I wish you luck.
