Most people carrying campers of any size (9, 10, 11') are over their payload and GVWR. Just don't overload your tires and axles.
My 8' Palamino pop-up in a 1996 Dodge 1500 weighed 7,000. GVWR WAS 6,400.
My 11' camper on a Chevy 3500 SRW was 11,150. GVWR wad 9,900. Same camper on a Chevy dually weighed in at 13,100. GVWR was 11,400. I had thousands of trouble free miles out of both rigs.