I concur with the above -- travel trailers are not good moving trailers. What your SUV can tow, and what it should tow, may be two different things. Trailers in themselves are weighty (even those touted as "lite" or "feather-lite"). Add in your stuff, and your SUV may blow a tranny in the midst of your move. What you'd spend to buy a travel trailer, you can use for motels.
What I'd suggest is renting a U-Haul-type truck that will hold what you own, and rent one of their car-trailers to put your SUV "4-up". You can put your overnight stuff in the SUV so it's accessible when you stop at night. You can find motels with "truck parking" available all along the Interstates. Hubby and I stayed in 5 different motels on our most recent trip, and only 1 motel did not have "truck parking" -- but it was also not right on the Interstate.
I used to live in CA, and on our east coast adventure one time, it was 6 days of driving comfortably. Moving our kids from CA or CO in the set-up described above (U-Haul towing one of their cars on a trailer 4-up), we did 550 miles the first day and it was hard travel. (It also didn't help there were two time-zone changes that day.). Keep that in mind as you plan. When we moved from CA to MO, we were towing, and kept our mileages under 450 when we could.
You probably don't *need* to, but if planning to stay in motels with truck parking, reservations are helpful. Call the place you are looking at, online, and ask them 1) how many trucks can park in their lot, 2) how is the access to said lot. Sometimes "truck parking" to them means you can park out on a street, other times they have nice pull-throughs. Sometimes "truck parking" means a lot of backing up -- not fun.
Donna