I would suggest getting a 9000 btu unit rather than the 13.5K. Unless you're going to camp in the southwest desert in the summer 9000 is going to be fine and maybe a little quieter (ie, sounds like a prop plane taking off not a bizjet). I'm assuming you have a roof vent in the center of the trailer (not the one in the bathroom) already. Those are a standard size so the a/c should be a direct replacement fit.
Take a look in your breaker panel. You will need a breaker for the a/c, If that's not already there its an easy install. You will also need a cable to the roof, a 120 Vac cable, not the 12V cable for a vent fan. Not sure if that is prewired already or not, but if not, the cable will be a bit of an issue to install, you'll probably have to run surface mount wiring. So you might want to pull off the vent and see.