Few have paid much attention to the organization of state military units just before and during the first few months of the Confederate government. Each state had its own military laws and militia organization, most adult men understanding their obligation to appear as required to the county courthouse for drill. The governor could call any organization into service for a limited period of time, which Southern governors did after secession (and sometimes before, as in the case of Alabama). These were assigned duties such as the occupation of Federal forts and arsenals.
By the way, I would be surprised if Florida had not received its allotment of Federal arms which had been distributed among U.S. armories in other Southern states.