Your route has good roads and no significant hills or bad spots. Stay on your route and you will not have any problems.
The reasonably priced fuel opportunities on your route are few and then vanishing. Cortez Gas just north of the 54/70 bypass and 82 junction north of Alamagordo is the last cheap fuel point. After that it gets more expensive as you go north. There is no Diesel between Carrizozo and Vaughn and none I recall from Vaughn to Las Vegas. Getting fuel in Las Vegas is best for your rig at the 84 and I-25 junction south of Las Vegas, the only almost truck stop in the area. In Las Vegas it involves getting off of the interstate and maneuvering into stations that are not RV friendly.
Scenery along the route is not bad. For some parts you need to look to the mountains instead of the road side, but there are some grand vistas along the way.
As far as places to stay there is Storrie Lake State Park in Las Vegas, Valley of the Fires near Carrizozo, and RV parks in Alamagordo.
I have a similar rig to yours and it is a 7 hour, 5er in tow, drive from Las Cruces to Las Vegas. If you start the day in Las Cruces you may want to plan accordingly.