You need to run the NPC on a few universities - Duke, and a few others - to have an idea of what budgets are expected. Decide what you’ll be able to afford by stretching but without compromising retirement or other kids’ college. Then, provide the range (35-45K?) to your child. Tell her that it’s impossible for you to go above that amount, but you’ll gladly help her research the schools she may like that fit within budget.
UF is very selective so make sure she also applies to another university she likes.
Duke won’t offer merit, but other universities with common traits to Duke may offer merit and be of interest.
Emory is an elite private in the Souh, and it offers merit (they also have another option with Oxford).
Miami Ohio has a great campus and great merit, is rather conservative and preppy.
If she wants warm weather and is a NMF, there’s USC in California.
If she wants a great honors college with good scholarships, top students, and a Southern atmosphere, there’s USC Columbia and UAlabama.
If she wants basketball, Temple, Gonzaga, Louisville, Syracuse, are basketball powerhouses and offer good merit aid.