With the dry weight of the camper only 400 pounds less than the towing capacity of the vehicle it will be virtually impossible for you to stay under the MAXIMUM weight your vehicle is rated for. In addition to the dry weight of the camper you have to add the weight of any passengers, pets, or other cargo in the vehicle that was not original equipment. Then add the weight of the hitch. Figure 50 pounds for a battery and 20-40 pounds for propane, depending on whether you have one or two tanks. That's towing with NO water in any of the holding tanks or even bottled drinking water (8 pounds a gallon).
Good information is available in the Trailer Life Towing Guides:
http://www.trailerlife.com/trailer-towing-guides/