Mapquest estimates around 16 hours from Houston. Single motel rooms are now selling out with it just a month away. Campsites, the same.
A nice detour that is not too far off track is Dixie Gun Works. In addition Shiloh Battlefield "near" Memphis is a worthy addition to the trip. This is the approximate date (April 6) of the battle so you see the area the way it was, more or less, in 1862. Shiloh alone is worth the trip.