fithp,
Your idea sounds perfectly ok and reasonable.
If you purchase a PUP from a dealer, the dealer will install the correct hitch and do the wiring for the trailer.
If you purchase the PUP from a private individual, you can take your vehicle to a good hitch installer company and have them install the hitch and wiring so it's done right and you don't have to hassle with it.
We owned a Chevy Mini-Van that towed our PUP for 6 years. Actually, I had the hitch and wiring installed some time before we even considered a PUP because I needed to tow a utility trailer when I gave up Pick-up trucks for a while. I thought it would be impossible to find a hitch that would fit the vehicle, but they matched one perfect. Turned out to be a flat hitch which mounted to the frame perfect. It would never tow a regular trailer but worked great for the utility trailer and later the PUP.
In Indiana, if the trailer is under 3000 pounds (fully loaded), you do not need to have brakes on the trailer. Check your state laws about brakes on your trailer. It does vary between states.
We did not go on long term trips, like ... months at a time ... but we did travel from Indiana to Maine, to Florida, to Alabama, to Kansas, to Wisconsin and Michigan and pretty much every where else in-between over those 6 years.
I think your idea is sound, and I think you'll have a lot of fun.
Here's a few photos from days gone-by. Sometimes I do miss the PUP, but never missed my first or second travel trailer.
This is Maggie. She (was) a concrete 100 pound goose. She traveled with us all the time and became a photo-hog. She was into travel long before the Travelocity Gnome became famous! Those were the days when I was a lot younger and a lot stronger than I am now, and moving Maggie around was no problem. Maggie got stolen from our house. We nave have Maggie 2, but she doesn't travel with us. We're living in a completely different house now and Maggie 2 has successfully guarded our front door for 7 years now!
I know, I'm kind of "off topic" now, but just wanted to make a couple points by sharing the photos:
1. Your plan is very do-able.
2. You will have a fantastic time (in your own way) when you make your trip exclusive your own.
3. And ... it's OK to break the "norm" and have fun doing your own "thing".
Maybe it's because of the crazy freedom we had with the PUP that made it so special!
Good luck in your search and decisions!