If I remember correctly, if you change addresses you must notify the Florida Dept of Agriculture and Consumer Affairs (or whatever it's called) of the change. For a nominal fee they will send you a new permit using your old information, and you may continue using the old one until the new one arrives. But, double check that before you start toting in Texas.
I'm sure it's a smoothe process, since I had researched it a few months ago when I was considering moving.