Depends ... on ... where you store/secure your gun/ammo while traveling.
If you take the I-10 corridor in a privately owned conveyance: No problem, as long as your fire arms are out of sight and you don't have a criminal record.
As for your incomplete question (what kind of gun, and how are you traveling) I suspect this to be another troll post since Florida has no "gun perm."
Your FL CCW is good in 35 states, to include every state if you plan to take IH-10 westward to get here. Hell, you can drive as far north as the Maryland line or west until you hit California or Nevada and be good unless you wander into Illinois...
Just be sure to check the laws in all the states you'll be traveling through!
For all other firearms, keep 'em unloaded and stored away.
I've done that trip on numerous occasions, it's nothing to worry about.