It would have to be the federal DOL, since Florida doesn't have one. Plus, my understanding is that the federal DOL will pursue straight-time pay only to the extent of the federal minimum wage, which is lower than Florida's MW. Also, in a small claims suit, you can sue for damages up to at least twice the unpaid wages, which the federal DOL will not do.
All of that to say that small claims is your better option. Most likely faster, also.