I was in Saline Valley last November... great place.
The road in from Big Pine is ok. There are some narrow shelf roads coming in from the north but wide enough for a dually & camper. Just keep an eye out for oncoming traffic, as it will be a tight squeeze in places for two vehicles to pass each other. I would highly recommend airing down your tires if possible, to make them less resistant to punctures. Just because you're bringing two spares doesn't mean you want to have to use them, right?
I didn't think the road was particularly challenging in the traditional sense (rockcrawling-type stuff), but rather it is riddled with washboards and just enough (small) rocks to shake, rattle & roll your whole outfit. Double check your camper's cabinets, drawers and anything not secured as you go down the road. Things will shake loose, fall out, fall over, etc. Everything in your camper will be going through a washing machine effect basically.
I would also suggest finding out the very latest road conditions as you're headed out the door. Last year there was a significant rockslide over the trail (on the southern side of the SV sand dunes) and we had to creep & crawl our way over it, in the dark. Not a lotta fun, lol! And there were three different "Road Closed" signs on the road, but we were told that these are more of a deterrent to the casual traveler and that the road is always open, so we drove around them and kept on going like everyone else.
Other than that, bring some airplugs for all of the military jets doing fly-over excercises in SV and leave the bathing suits at home. You'll be over dressed if you wear one. There was a renovated old school bus there last Fall, who apparently made it in with no problems, so you should make it in ok. Personally, I liked the upper springs better for the solitude and pools, but the lower springs were really cool, set back in the trees with grassy lawns all around. That was party central during our visit.
Great place, hope you have a great trip!
.