Go to a beach which allows fishing, bring a fishing pole, and make sure you throw a line in the water. I'm not a lawyer, but the law plainly says it's legal:
WEAPONS AND FIREARMS
790.06 License to carry concealed weapon or firearm.
Summary: Illegal without a permit.
Summary: Illegal where otherwise not allowed by law.
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:
(h)A person engaged in fishing, camping, or lawful hunting or going to or returning from a fishing, camping, or lawful hunting expedition;
(4)CONSTRUCTION.--This act shall be liberally construed to carry out the declaration of policy herein and in favor of the constitutional right to keep and bear arms for lawful purposes. This act is supplemental and additional to existing rights to bear arms now guaranteed by law and decisions of the courts of Florida, and nothing herein shall impair or diminish any of such rights. This act shall supersede any law, ordinance, or regulation in conflict herewith.