You have gotten some great advice. I would hit a CAT scale when you are fully loaded and ready to go. Then check rear axle weight rating, rear tire rating, and your rear wheel rating. I would be interested in knowing what exact tire you have on the truck now. People here just want you to be safe and enjoy the ride.
Just so you know, I went this route once with a 2500 truck. I put 19.5 tires and wheels on it before ever loading the camper(1150). Along with a bunch of other items. I soon got a 3500DRW and I love it. Stress free driving. Good luck.