Route

I hope I didn't create the impression that Nevada has "speed traps."  It doesn't.  The speed limits in the rural towns are not unreasonably low and the enforcement is not because the local jurisdictions are trying to use speeding tickets as a revenue source.  The strict enforcement is for safety.  For example, U.S. 50 between Fallon and Carson City is one of the most dangerous stretches of highway in the state.  Car v. wild horse collisions are common.  We had a double fatality near our home in Dayton due to excessive speed just about a month ago.  It is common for people to out drive the illumination of their headlights at night so when a horse suddenly is in front of them, it's through the windshield before they even can get their foot on the brake, much less slow down.  

Stay off of I 10 in Calif. Too much traffic. Stay east of the Sierras. Too much traffic.  395 is a good road to pull a trailer on.  Or any of the North - South thru Nevada.  Do not pass a gas station if you are going thru central Nevada  .  Beautiful scenery and hardly any traffic.  Probably be a wind from the north this time of year.

Thanks for all the great replies. I think we will fly instead.

Now that I think about it, US-95 north (and then 395, etc.) might be the more fun route. I-5 through the central valley in California might save you a couple hours, but gawd is I-5 an awful road to travel. I've never had a trip north or south on I-5 where there has not been some kind of "incident". There has always been at least one nut job on the road trying to get around traffic and doing something stupid. The other side of the equation, is knowing that the incident is going to happen, and you are tense waiting for the shoe to drop. I just hate driving that road.

I believe that the route should be I15. I95 is on the east coast. That would really be going the long way around. 
I took a quick look and I15 to I84 is one alternative. I10 to Las Angeles and I5 to Oregon is the other. Interstates usually don't have very steep grades which some non-Interstate highways can have e.g. Tehachapi Pass along highway 58 in California. I pulled a U-Haul trailer up that once towing with a Honda Civic CVCC wagon in 1984. That was a real challenge for a grossly overloaded and underpowered  tow vehicle. I had a bumper hitch and had to reinforce it with rope tied to the roof rack to keep the hitch from sagging. We sure did not set any speed records on that trip and had to turn the heat on and open the windows to keep from getting roasted in order to keep the engine from overheating on that climb. It is not something I would ever repeat but I did not know better at the time.

Edit: Yes, there is a US 95 there. I had forgotten. Sorry for the confusion.