We drove from Georgia to Disney World last Labor Day while everyone else was going the opposite way of Frances. Still had a great time even with a 24 hour lockdown.
If you are concerned, here's some advice. Take bottled water with you. Also, take an extra cooler. You can get a cheapo styrofoam one. Pack clothes in it on the way down. IF there's any threat of bad weather (and Disney will let you know), get your ice ASAP. Our machines ran out - we did have enough ice but had to wait a little.
Take diversions. Board games, cards, whatever. IF you get into a lockdown, you will have Disney movies (over and over and over again), ESPN, and panicked local newscasters. Gets extremely boring.
Since you are driving, you can easily prepare a "hurricane" bag. Just in case. Hope you never need it but have it for your peace of mind. Oh - and IF there's any threat of a storm, make sure you have a full tank of gas before it hits. We did all that and even though our weekend getaway was mostly spent in the room at Pop Century, we had a wonderful time with each other. My entire family had to evacuate from the Florida Keys just the weekend after this due to Hurricane Ivan. They all went to Disney World because they felt it was the safest place to be. I didn't have to worry about them at all.