With OE 17" wheels you can get Toyos rated to 3950lbs.
I'm (was) hauling a 4klb+ 8.5' camper on a sb truck. Pulled a 6k or so trailer with 8" hitch ext pretty heavy tongue to AK, no issues.
My truck needs a sway bar for sure but handled the load just fine.
You will be better w a long bed as your cg of the camper will be another 18" fwd.
There are plenty of "short bed" campers that will fit on a lb truck and allow you to hook up the trailer to the OE hitch. Also some, like my old AF have no drop down overhang. They are not lower than the truck bed. Gives a lot more room to hook and haul trailers.
If you get a non slide 8-9' camper there are many that will be around the 3klb weight which is easily doable with your setup and good tires.
The weight cops on this forum will say differently though.
2500 3rd gen ram does not even know there's 1500lb in the bed. Just hauled a load to the dump. First time ever weighing the truck. Truck was 7640lb empty and just over 9k loaded and with no air in the bags it did not even squat at all. Barely moved.