I did a month long rental trip earlier this year and my cat went with me. Granted, it was in a motorhome, which would be a bit different from a trailer. I made frequent stops so she could get off the bed to use the cat box, eat some food and get some snuggles. She stayed on the bed once she realized it was not a good thing to move around while I was driving.
I always had her harness on which had her rabies tag and contact information on it. She's not the escaping type of cat (crippled in the back end so she doesn't move too quickly), but I still wanted that info on her, just in case. Stuff happens.
I took her outside a few times, but she was always on her leash, which was attached to her harness. I tested her out on it at home before I left.
If Lucy's still around when we get the trailer (she's 14+, so kind of doubtful with her other health problems), I plan to put the litter box at the foot of the bed. For traveling, she would travel in a pet carrier in the truck as she'd be safer that way. I'd be stopping every few hours for breaks for myself and for her, so I'd let her loose in the trailer. We both would need those food and pee breaks!
The other kitty we just acquired - not sure if I'd take him with me as I don't trust him to stay in the trailer when the door is opened. Will your cat want to escape from inside?
I also traveled with copies of her current medical exams and shots, in case I had to take her to a vet while on the road.
And a small shirt that we got for her when she had surgery on her belly area and wasn't supposed to go near the stitches. It also helped keep her warmer and the motorhome got a bit nippy at night as I like to sleep in a cooler environment. The shirt doesn't bother her at all.
I really enjoyed having her with me on that trip. She was a great traveler and didn't complain once.