I have to say that newer DRW GVWR is probably closer to 13-14K but they also weigh more. I've also switched to a DRW due to no longer needing the SRW as a daily driver. I can now get by with a DRW. It gives me more room for error and no doubt it's safer with the awesome brakes of my F450, and turns tighter than the F350 SRW by far.
My SRW had a GVWR of 11400, and my camper was a similar weight. Since I needed the SRW, I upgraded my tires/wheels to 19.5s and it handled really well. I did pay very close attention to how much I carried even down to how much water I carried, and dumped early in the trip home. The truck handled noticably different with empty holding tanks.
You'll likely be overweight, but it is doable. If you go with a bit smaller camper and watch how much you carry, you'll have a bit of wiggle room.