I'm looking at shooting fall foliage in North Carolina, Virginia and Tennessee about that time or I'd offer to take you through the Merritt Island National Wildlife Reserve here, north of the Kennedy Space Center.
Sanibel Island, south of Clearwater by some distance, actually next to Fort Myers, has the Ding Darling wildlife refuge and is one of the better spots to shoot birds, with restrictions on time and location, so research is in order.
A commercial tourist attraction, the St. Augustine Alligator Farm, is one of the top sites for shooting newly hatched waterbirds in season. They open the doors to photographers before tourist hours so they can shoot without interruption.
Any drive that parallels water anywhere in the state will give you an opportunity to shoot water birds. Inland you can see hawks, eagles, vultures, sandhill cranes and many songbirds, as well as other wildlife.
It's 792 miles--1275 kilometers from Pensacola in the far west to Key West in the far south. Ft Myers is 141 miles from Miami or 251 miles from St. Augustine. On our interstate highways and state roads you can average about 55 miles per hour, even though the speed limit tops at 75 on the interstate. You will need to drive if you want to get anywhere, bus service is relatively poor and train service very limited.
If you fly into Miami or Orlando then you can easily cover two to three of the five main wildlife areas. From Miami you have the Keys, the Everglades and Naples to Ft. Myers, possibly Merritt Island. From Orlando you can do St. Augustine, Merritt Island, the Clearwater area and possibly Ft. Myers.
Our safety suggestions are about the same as yours. Keep your gear locked in and out of sight in a car when you park. Hopefully you will have a secure locking case for when you might be out of your hotel or motel room. A cane or a sturdy monopod will deter all but a robber with a gun and you aren't likely to see many of those out in the wildlife areas. Your biggest threat will come immediately after you drive onto the freeway (or toll road) after picking up your rental car. Tourist from overseas have been targeted in the past by organized thugs who watch for travelers coming in from international flights, follow them until they get a car, signal to confederates who are cruising around to follow the rental car--finally they smack into the rental car as if by accident and rob the unsuspecting tourist when they get out to inspect the damage and exchange insurance data. Have a cell phone with you, test to make sure you can contact 911 before you leave the airport.