Uwe -
Salamander-wise you will likely be limited in the Fort Meyers area. You might be able to find some Notophthalmus v. piaropicola in some ponds by netting vegetation. You may also pull up some dwarf sirens, lesser sirens, greater sirens, and amphiumas this way. A little bit north of Ft. Meyers you may be able to encounter A. talpoideum. The Panhandle and northern peninsula holds the rest of the salamander species.
As has already been stated you shouldn't have a problem seeing gators, they are pretty much everywhere. Turtle-wise, well, I am not the best to ask, but you will likely see sliders and cooters maybe some softshells basking on logs primarily in the fresh water areas. In the salt marshes and even on beaches you have a chance of seeing some diamondback terrapins which are a truly neat animal to see.
Somebody else could probably say more about snakes, but there are quite a few to be found in FL. If you can find a mud snake you know there are likely sirens and amphiumas in the area, or vice versa.
I hope that helped...some. The herping I have done there has been restricted to the panhandle and the north, so I'm not terribly familiar with the Ft. Meyers area. Just because it is Florida though, you will likely see at least a few cool herps.