Your Florida license is valid in Georgia until you have established residency, at which time you must apply at your local Probate Court for a Georgia Weapons Carry License.
Georgia makes no legal distinction between open and concealed carry, all handgun carry* requires a license.
Carrying on your property, at your work, or in your car requires no license, but as soon as you step outside those confines you must have a license or 'transport' the firearm.
Unauthorized locations are defined by law, OCGA 16-11-127.
* handguns with barrels over 12" are not considered concealable and need no license; unloaded and encased is considered transporting and again no license required.
p.s. 0790.053 "... It is not a violation of this section for a person licensed to carry a concealed firearm as provided in s. 790.06(1), and who is lawfully carrying a firearm in a concealed manner, to briefly and openly display the firearm to the ordinary sight of another person, unless the firearm is intentionally displayed in an angry or threatening manner, not in necessary self-defense..."
--- which means there would be no 'brandishing' if it were to be momentarily visible.