If you are here on orders and only fishing from shore, I believe you are recognized as a resident and only need the Saltwater Shoreline License which is free. Probably still only available at Tax Collector's office w/copy of your orders and Military ID.
The Military Gold Sportsman License for $20 which covers hunting and fishing from a boat is a great bargain.
Being stationed in Florida, you are considered a Florida Resident under FFWCC's Florida Residency Requirements. So, are you wanting to fish from shore or a boat?