Certainly the drive from Savannah to Miami is doable in a day. You can even make it to the Keys in that day.
One thing I forgot to mention earlier is that late November is wintertime in the higher elevations.So, it definitely possible that some parts of the Smokies will not be accessible then. Elevations in the Smokies range from 876 ft to 6643 ft., so weather there definitely varies a lot. There is also the possibility of closures on the Blue Ridge Parkway. Closures actually are more likely around Asheville because the BRP near Asheville reaches its highest elevations. None of this should dissuade you from doing this trip, but it worthwhile to keep all of this in mind as you make your plans.