Don't quote me, but I believe (like most gun laws) that this permission varies by state, county, city, etc. I'd check with a LEO friend on the rules where you live.
LEO's are just about the worst people to ask for legal advice. Also, Florida has complete state preemption of firearms laws.
Here's the relevant statutes:
Statutes & Constitution :View Statutes : Online Sunshine
790.001 Definitions.—As used in this chapter, except where the context otherwise requires:
(17) “Securely encased” means in a glove compartment, whether or not locked;
snapped in a holster; in a gun case, whether or not locked; in a zippered gun case; or in a closed box or container which requires a lid or cover to be opened for access.
Statutes & Constitution :View Statutes : Online Sunshine
790.25 Lawful ownership, possession, and use of firearms and other weapons.—
(3) LAWFUL USES.—The provisions of ss. 790.053 and 790.06 do not apply in the following instances, and, despite such sections, it is lawful for the following persons to own, possess, and lawfully use firearms and other weapons, ammunition, and supplies for lawful purposes:
(l) A person traveling by private conveyance when the weapon is securely encased or in a public conveyance when the weapon is securely encased and not in the person’s manual possession;
Statutes & Constitution :View Statutes : Online Sunshine
790.33 Field of regulation of firearms and ammunition preempted.—
(1) PREEMPTION.—Except as expressly provided by general law, the Legislature hereby declares that it is occupying the whole field of regulation of firearms and ammunition, including the purchase, sale, transfer, taxation, manufacture, ownership, possession, and transportation thereof, to the exclusion of all existing and future county, city, town, or municipal ordinances or regulations relating thereto. Any such existing ordinances are hereby declared null and void.