I just drove from NJ to WA at the beginning of May. My SO relocated out to be with me. We drove it together. I can attest to the draining of energy from continuous days of driving. And we shared the driving duties!
I would highly suggest you limit your driving time to 8 hours or less each day, that's including the stops for meals, potty breaks and such. And taking the time to visit and relax along the way is a good thing too! We tried to get hotels with pools and swam each day to ease the stiffness from sitting in the car.
Another suggestion is to build in an extra day in case you start to get behind as you drive. We got behind, but with two of us, managed to do a really long day to make it up. You won't have that luxury.
As to route, may I suggest I-90 until western MT, then drop down at Butte on I-15 into ID? Then pick up 84 to Boise... You'll have a pass by Bozeman, MT, one before Butte and then one from MT to ID, but you're kinda stuck with going through passes to get over the Rockies. Fortunately the traffic out West is light enough, any pass you go over, you'll see other people struggling too, including the big trucks!
edited to add: Have fun! It's great to travel that far, we had a blast!