If you want to safety tow that camper, I'd get a F250/350 Tremor. Or get a lighter trailer.
8700 pounds dry- that's manufacturer's optimistic weight. Plus batteries, propane, water in the tank, all your camping gear, kitchen gear, luggage, food, beverages. You can see how this will spin the dial to over 10,000 very fast. Wiser folks than me say you shouldn't normally tow over 80% capacity for safety.
Also, on the weight distribution hitches- they push some extra weight to the truck's front axle, but they don't give you any more cargo capacity.
For what it's worth, I've towed my Jeep for many hundreds of miles and it did great. I'm leveled and sagged a lot. I'll get airbags before I do it again. That was with 8,000 pounds on the CAT scale.