Look at the reputation of ALL the schools in your area before making the decision, send her to the one with the best reputation for academic support and emotional support as the highly intelligent are often victims of bullying.
In the places I grew up in a lot of the private schools had some really nasty reputations- they were the dumping grounds of the public schools! Once a kid got kicked out of all the public schools the government subsidised their education at a private school- some of those private school kids belonged behind bars!
Here it is kind of a catch 22- both the private AND public schools are NOT the type of place I want my children! My local public primary school has a good reputation, but there are rumours that it will be shut down before my son is old enough to enrol- if it is he is going private, to a religious school as these are only two schools within reasonable proximity to my place that I would trust!