Your route seems to be a pretty good one....once you get down south, you should be fine. Could there be a serious freeze? Sure, but you would be living in the RV, and have the heater running, so you should be fine.
You will also be able to monitor the weather channel or check out areas on the computer, so if you see it' getting too cold in one area, you can beat feet, and head to another which is supposed to be warmer!
Just to be sure, open cabinets at night, so the heat from the rooms gets down under there, where the pipes are.
You may also want to get an inexpensive space heater for a basement area, if it's got some items that might be damaged with a freeze.
Have a great trip!
