Welcome to FT, Larry ^
Assuming an on-time arrival from DFW, 1 hour to get past passports (very likely, especially in peak season) and that, by that time, your bag would be already on the belt, you would still have nearly 1 hour to re-check (being NAP a domestic flight, check-in closes 40 minutes before scheduled departure) and go through security again, which shouldn't take long (T1 is normally fairly efficient). So, indeed, you could make it.
G