The biggest concern would be the cat getting loose, and getting lost. I'd recommend using a travel crate for the cat when you are driving. Get a larger one, so there is more room for it to stretch and walk around. Then bring it from the TV to the TT before you open it. You can also put a small little box in the crate....don't worry, you'll know when it's been used:)
I'd also keep the cat in the crate, when you leave the trailer for the day, just in case it happens to be one of those destructive types, and the curtains end up shredded!
Lots of people travel with cats, and as mentioned, it will depend on the cat....so you may want to try a few short weekend trips to see how it behaves, before going on a long trip, or you might all end up miserable!:(