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Your truck should weigh 5,841 empty (short bed?).
Add the 1200 lbs of people and cargo and you are up to 7041. Better throw in a couple hundred lbs for fuel... you are up to 7241.
Your GCWR is 13,500 lb, so 13500-7241 = 6259 lbs left over to haul.
You also need to look at the 8800 lb GVWR. 8800 - 7241 = 1559 lbs (don't let your trailer hitch weight put you over on this number.
It is best to weigh your truck loaded with everyone in it. 1200 lbs is only 300 apiece for 4 people and all their stuff.
nafzimo gave you the truck numbers, so I'd just like to caution you that the RV "dry" weights are often stated way below the actual weight of the trailer. A better number to use is the trailer's GVWR. After adding options (a/c, awnings, slides, etc.) and all your "stuff" (pots, dishes, clothes, propane, etc.) you'll probably be close to the trailer's GVWR.