Hi Steve & Lynette,
We did that very path in April this year in our 41' motor home, 12' 6" high pulling a Jeep. It is such a wonderful drive you will want to divert to it from now on. Since it was the first time we took it, we spent nearly 3 weeks, stopping at most of the attractions and every campground.
There are 3 free NP campgrounds along the Trace. They have no facilities. We stayed in each of them from overnight to 5 days. There are hiking trails, museums and many special points of interest.
In addition, you can drive off the Trace not very far to reach many other facilities. In addition to the 3 free campgrounds, we stayed in 3 state park campgrounds in Mississippi that weren't far off the Trace. All were beautiful, had full services and one included a free round of golf at a nearby course.
Enjoy your time on that road as your rig will have no problems. Once you experience the Trace, you will wish all roads where that way.