According to the Jeep website, the 2014 model only has a 2K towing capacity. Yours might be different depending on what year it is. However, the Patriots have always been a small SUV so I can't imagine that the towing capabilities would be substantially different with a year model change.
The weight limitations alone will limit your trailer selection to the smallest size available with the least amount of options. By the time you pack for any kind of extended trip, I would think that you would be well past the capabilities of the tow vehicle.
Look for nothing more than a 8' box from any of the manufacturers, or a alternative style camper such as the Livinlite 10.0.