I'm going to insert a counterpoint...
If all I wanted was a place to sleep, and it were just one person and a small dog, I don't know if I'd want the trouble of a trailer. It limits how fast you can drive on interstates (55-65 versus 65-80, depending on locale). It limits where you can park. It limits the kinds of places you can go- back roads and urban core locations are cumbersome with a trailer. It requires extra time and maintenance. A pick-up with a cap, a minivan, and some SUVs can make into a nice bed.
I've done it both ways. When I was single I traveled and slept in a pick-up with a cap, a van, even the back of a Subaru wagon. For quick overnights wherever (rest area, forest road turn off, friend's driveway, gas station parking lot) it was fine, and I felt light
on my feet. The van was the best because if I ever woke up and felt uncomfortable with the surroundings, I could get into the seat and drive off without getting outside the vehicle.
On the other hand, in a campground or someplace I can spread out outside the vehicle, the extra space and comfort of a trailer is worth the trouble. I had a small tent trailer that I sometimes took with me for that kind of trip, usually several days in one place. Now that I'm married with kids, that's all I do- no more sleeping in the back of the car in a parking lot. My wife vetoed that idea! I will observe that a 5x12 is a pretty big trailer. For that size, you might as well get a real travel trailer.
Having said all that, I totally understand we're all different. I have done some unconventional things that others advised against, made great memories, and learned from every experience. I moved to Arizona from Maryland 33 years ago in the middle of winter, straight out of college, with everything I owned in a VW Beetle. I rigged up a bed on the passenger side that sat on top of the seat backs from the windshield all the way to the back and slept my way across the country. Every morning I had to scrape ice from the inside of the glass as well as the outside. Do I regret doing it? No. Would I do it again? No.
Best wishes, whatever you decide!