The post by draybook is the shortest route to take. the only thing i dislike about it is you will be driving south of Dothan Alabama on a state highway with red lights until you reach interstate 10 in Flordia.watch out for mapquest it will have you going on more state highways with stop signs and red lights only because it is shorter.
I take 78 East to Birmingham,20 east to Atlanta,in Atlanta just after you pass Six Flags take the bypass south around Atlanta, get on 75 south, turn left to get on the Florida Turnpike ( about 1 hout to go) , then follow the signs to Disney.As most people know Mississippi still has not finished 78 all the way to Birmingham so there is a short streach with some red lights just before you reach 20 but after that it is all interstate from there. I hate to go through small towns with slow traffic.