Take the dog, trust Me.. (after living on the road for 300 days a year for 15 years) the companionship will make your trip much more enjoyable, It would suck to do this and then be so lonely you miss out on things that the loneliness distraction caused.

There is alot to see in the lower 48 and not all of it has an interstate built next to it.. so travel some of the US Highways.

The down side would be.. it would limit the hotels you could stay in.. but if you are going on a budget.. budget hotels allow pets.

I am an over the road semi driver. Not one of the most exotic careers in the world but adequate to the point of living a respectable life. You might consider that career move for a while. I am sure there are a few places to get you up and running in SLC. My first driving job was for a company based in Salt Lake.

Good luck in your travels
Jeff