If you have a concealed weapons/firearms permit/license from either Ga. or Fl. you may carry concealed upon your person in either state while in your vehicle.
In Florida you may have a loaded handgun in the vehicle as long as it is securely encased. Such as in a glove compartment, center console, briefcase etc.
790.25 Lawful ownership, possession, and use of firearms and other weapons.--
(5) POSSESSION IN PRIVATE CONVEYANCE.--Notwithstanding subsection (2), it is lawful and is not a violation of s. 790.01 for a person 18 years of age or older to possess a concealed firearm or other weapon for self-defense or other lawful purpose within the interior of a private conveyance, without a license, if the firearm or other weapon is securely encased or is otherwise not readily accessible for immediate use. Nothing herein contained prohibits the carrying of a legal firearm other than a handgun anywhere in a private conveyance when such firearm is being carried for a lawful use. Nothing herein contained shall be construed to authorize the carrying of a concealed firearm or other weapon on the person. This subsection shall be liberally construed in favor of the lawful use, ownership, and possession of firearms and other weapons, including lawful self-defense as provided in s. 776.012.