Fine to root now as long as you do it indoors where it's cooler, or when it's cooler outside. Higher Florida humidity will actually help it root better. Just toss it in some perlite, vermiculite, or dryish seed starting medium and it'll do it's thing.
You'll definitely want varieties that can tolerate Florida humidity. Brown Turkey is a very blah variety unless you're using it as rootstock for grafting, just an FYI.
Cole de Dame is a top-tier fig that tolerates high humidity very well. Improved Celeste is also a good choice (has to be the improved one), along with any of the LSU varieties.