moving on up

This is direct from www.ramtrucks.com using the vin number of the vehicle.
max payload 1485 max towing 8000

funfinder gvwr 7,400 camper weight is 5,185 hitch weight 400
passport gvwr 5,200 camper weight is 3,595 hitch weight 385

I don't see myself adding 1500 pounds of gear to either of the weights listed above maybe 500 but that's even high.
We're talking linens, clothes and we usually grocery shop when we get to where we are going so minimal food.
Couple of folding chairs and some cooking utensils round out the list.

so by conventional thinking adding my wife and my weight and the weight of the mutt we come out around 600. It's a big dog (yeah right).

subtract that from the max payload still leaves almost 800 pounds.
Yes I know the tongue weight does not include propane and battery so add 120 for that and say 200 on the high side for gear. were at 700-800 tongue weight.
Still within the limits of the vehicle.

It is good you are looking at the numbers. Use 15 percent of trailers gross weight for the tongue weight plus another 75 pounds or so for the hitch. You could easily be nearer to 1000 pounds tongue and hitch weight. You will add far more than 500 pounds of stuff in the trailer as water weighs 8.3 pounds per gallon. If the tank holds 50 gallons that is over 400 pounds just for water. Add your other stuff and you are at 900 pounds if not much more. It is so easy to keep adding things until they all add up to much more. About 20-25 percent of the tongue weight is transfered back to the trailer axles so there is a little wiggle room there as it relates to your less than 1500 pounds payload. You will be limited far more by payload than towing ratings. Also don't forget the other stuff you will carry in the back of the truck. I don't see how you could even think you will try to be at only half or three quarters of the trucks payload or tow rating that you refered to in your first post. The 800 pounds of 'still available payload' after your weight, wifes and dogs is likely insufficient or nearly so after adding in the tongue and hitch weights especially for the Fun Finder.