That's a good time to leave. Although you might want to start a few weeks earlier to try to avoid mid-summer heat on the WE, you probably don't care to see how late it can get cold in the southern Appalachians, like the first of May cold freeze that killed all the trees back some 10 years ago.
Also, beware: there are these things called either mountains or hills that will slow you down. 80 miles per day on flat ground may turn out to be 30-40 miles in Virginia, Kentucky, and Missouri.