I think the first thing you'd exceed, and probably the important thing, would be the tires. The chassis and drivetrain is shared with the DRW so that wouldn't be a limiting factor. But the tire weight rating and probably lower vehicle stability without Duallys at that trailer weight would be your bigger issues.
I would bet if you address the tires/wheels and maybe the suspension you could get down the road okay, but in my opinion it isn't that smart. You could trim back the trailer a bit and still pull a really nice toy hauler with a SRW truck.