There are two sections that deal with this, and both make it perfectly legal for you to carry a firearm in your vehicle. The first says that as long as the weapon is secured in your vehicle and out of plain sight, then it is legal. The second says that no person or employer can force you to give up your right to carry a weapon in your vehicle as a condition of your employment. They are as follows:
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.
790.251 Protection of the right to keep and bear arms in motor vehicles for self-defense and other lawful purposes; prohibited acts; duty of public and private employers; immunity from liability; enforcement.--
(3) LEGISLATIVE INTENT; FINDINGS.--This act is intended to codify the long-standing legislative policy of the state that individual citizens have a constitutional right to keep and bear arms, that they have a constitutional right to possess and keep legally owned firearms within their motor vehicles for self-defense and other lawful purposes, and that these rights are not abrogated by virtue of a citizen becoming a customer, employee, or invitee of a business entity. It is the finding of the Legislature that a citizen's lawful possession, transportation, and secure keeping of firearms and ammunition within his or her motor vehicle is essential to the exercise of the fundamental constitutional right to keep and bear arms and the constitutional right of self-defense. The Legislature finds that protecting and preserving these rights is essential to the exercise of freedom and individual responsibility. The Legislature further finds that no citizen can or should be required to waive or abrogate his or her right to possess and securely keep firearms and ammunition locked within his or her motor vehicle by virtue of becoming a customer, employee, or invitee of any employer or business establishment within the state, unless specifically required by state or federal law.