My F250 rear axle weight empty was 2750 lbs and 7000 lbs once we were in the truck and my AF811 was on the back. When I hitched up my 8000 lb enclosed trailer on a 28" SuperTruss and 10,000 lb WDH, the rear axle weight was closer to 8000 lbs.



Your truck's empty rear is about 500 lbs heavier than mine and the camper you want is about 500 lbs heavier than mine. I expect you will be close to 9000 lbs on the rear axle once everything is loaded and hitched.
You could still do this with the current truck's 10,000 lb AAM axle using 245/70R19.5 LRH PR16 tires and Rickson or American Force rims, but Vision rims are rated for 4500 lbs each and would be too close to their maximum to spend all that money.