Ive towed a few U haul trailers of all sizes (no auto transports yet) and generally are nice - their heavy but they are meant to last 40 years. Surge brakes work pretty good least the ones I had. Go slow take your time - you may be the rock in the river but im sure you will find most people just want to oogle at it anyways as they pass you.
Stop every so often at rest areas and check straps every time AND CHECK THE TRAILER TO BALL CONNECTION! every u haul trailer Ive used I was able to turn the big square tongue nut another click or two every time I checked it. No idea why it kept loosening up.
Also you may want to consider one of these:
https://www.amazon.com/StowAway-Tigh.../dp/B0001CMUV4
last trailer i towed from IL to OK all 534 miles of it all i heard was the hitch ratteling in the reciver at every pothole bump crack on the interstate. Wasnt just a rattle it was things you could feel in the floor as its bolted to the frame. Didn't and wont hurt anything but sure would have preferred it NOT to rattle - radio only goes so loud.