Your real world towing capacity is limited to the weakest link in your overall towing system ratings. You have weight ratings on your tires, axles, and hitch receiver. You also have a tow capacity rating and a payload rating. Most often, the weak link is payload.
Look at the tire / loading sticker on your drivers door post. It will have a number for "max occupant / cargo" weight (AKA payload). That is that particular truck's capacity to carry everything and everybody you put in it and on it. The weight of hitch equipment and trailer tongue weight count as cargo weight on the tow vehicle.
The trailer in question, will need somewhere around 1000 lbs of available payload. That is based on:
1. Average camping load (dishes, pots and pans, bedding, BBQ gear, camp chairs, groceries, water, etc) is 800 - 1000 lbs
2. Average tongue weight is 12 - 13 percent of loaded trailer weight. That trailer will be close to 7000 lbs loaded. Twelve and one half percent is 875 lbs. Tongue weight NOT being a constant number, yours could be higher. Tongue weight can fluctuate quite a bit. During any trip, mine can be anywhere between 975 and 1200 lbs, depending on fluid levels in my holding tanks.
3. Weight distributing hitch weighs about 100 lbs. Add the tongue weight, at a minimum, it will eat 975 lbs of payload.
If your tire / loading sticker says 1400 lbs (for example), that would leave you about 400 lbs of payload available for people, pets, aftermarket accessories, and cargo in the truck.
Here's a link to a calculator. Put in your numbers and see where it falls.