Her SAT score is great, but in and of itself may not get her a big merit scholarship, What is her GPA? Is she the best or close to the best student in her HS class? Is she taking the most rigorous course work?
The possibility of a full ride at any college, particularly UVA or Duke, is exceedingly slim. Are you sure about a full ride to UF? As noted above the only full cost scholarship there appears to be for students that are National Merit finalists. Does your HS participate in the Jefferson scholarship? Some of the UVA scholarships (and those at other places) require demonstration of financial need.
The best approach may be to look at schools she may be interested in and see if they offer pure merit scholarships. Set a realistic budget, as it may not be possible for her to go for free. But quite likely she can get a discount.