TexasCHLforum.com

http://www.handgunlaw.us/" onclick="window.open(this.href);return false;

You cannot carry a gun into any restaurant that serves alcohol in LA.
I think it was Alabama where you cannot have a loaded gun in the car unless you have a carry permit. Don't leave your daughter in the car with your gun unless she has a permit. You're not in Alabama for very long, unless you get lost, so, not a big problem.
Do you have a Texas permit to match your Texas DL? If not, Florida does not honor it. Florida requires you to have a "home state" permit for reciprocity, or, a FL non-resident license.

I made that drive over Thanksgiving. These are the only things I remember that were "potential trouble".
Check with the link above and read the details for yourself in case I missed something.