We drive from Shreveport all the time - I-49 to I-10. We leave after school (about 2:30) and usually get to Daphne AL by evening (it's about the halfway mark-just across the bay from Mobile). They have a nice Comfort Suites there (we've stayed there so many times that they know us now). Also a Hampton Inn right on the bay. Then we get up early in the AM and get to Orlando by 2:30 PM. Takes us about 14 hours to drive. It's a pleasant drive. You can cut off along the Gulf coast around Biloxi - Gulf Port. It adds a little time, but it's not bad. You cross the Mississippi River in Baton Rouge (don't go to New Orleans, take I-12 to bypass it and save time). Mobile Bay is pretty, too, and you can see the USS Alabama.
Or you can take I-20 to Jackson MS and cut off on Highway 49 to Mobile. It's about the same. You can go by the Battlefield at Vicksburg on the way to Jackson. You cross the Mississippi near Jackson. This way takes about the same amount of time since you leave the interstate and take the state highway (or US highway, can't remember what it is).
You can go on towards Pensacola or Tallahassee, but it makes it a bit harder. We drove all the way from Orlando to Shreveport on Christmas Day one time. It was a long trip. We also drove all the way from Shreveport to Ocala one time - very long trip. Hotels in Pensacola are not as close to the interstate. More in Tallahassee along the interstate. If you can make it all the way to Gainesville (I-75), there are a bunch of hotels around there. It's a bit of a long drive in the FL panhandle. If you can get to Gainesville, you are only about 2-3 hours away from Orlando. There are a few rip-off gas stations along this long stretch between Pensacola and Tallahassee.
Just after you get to Ocala, you turn off on the FLA Turnpike and you can see all the orange and grapefruit groves along the highway. The Turnpike is not that expensive - about $2-4 each way.