Nothing wrong with taking the bike with you on a trip in your trailer. My wife and I do it all the time. It makes long trips much more comfortable and we still get to do all the riding we want to do at our destination. On the 100 plus degree days of summer, there is no better combination. Plus we can take the kids and the dog too.
We have a 12 x 6 enclosed trailer we picked up used pretty cheap. The former owner had it pimped out for 4 dirt bikes. He had the inside floor and about 2 feet up the walls covered with Line X and then covered the rest of the inside with marine paint so it can be douched out. I mounted one of those "The Clamp" cycle stand up braces in the center of the floor just a few feet back from the nose. Works great. The trailer also has a side door that makes it real easy to check on it during fuel stops and when I need to top up the Rockets fuel too.