Remember, the roads will be packed on Labor Day weekend. It might take you an extra hour or two to drive to the Florida border.
You have to drive at least a half hour into Florida to get to the first decent area with lodging. That's Lake City. Good stopping off point if you stay with the major chains along I-75. Unfortunately, due to no reservations, and the overflow crowd from a Florida State football game, we got stuck at a sketchy Days Inn off I-10. Ten miles round trip out of the way.
And I just checked. Yes, Florida State is at home on Labor Day weekend. Meaning overpriced rooms. If you can get a room. (I know Lake City is an hour east of Tallahassee. But that's how popular FSU football is.)
However, if you make it that far, you are less than three hours to WDW.
Another option is Valdosta, GA. That's about 15 miles north of the border. Much larger area, and all the chains are there. Under your circumstances, I'd probably stay there. Or maybe a little farther north (Tifton, Macon).