If a FL permit isn't good in Georgia, I could be in deeeeep doo-doo. Seriously, though, the State of Florida's own web site says they have reciprocity with GA.
The trick to reciprocity, though, is that while you are in State X woth a permit from State Y, you must behave as if you had a State X permit. If State X does not allow carry in church, for example, while your own State Y does, then you can't carry in church in State X.