In my opinion, the Yukon is not the right tool for that job.
I tow a camper that was listed by the mfr as having a 5700 lb empty weight and a 600 lb tongue weight, and is 32' from ball to bumper. A trip to the CAT scale showed those weights to be pure fantasy. Minimally loaded, it weighs 6500 lbs and puts 750 lbs on the tongue. Loaded with camping chairs, chocks, food clothes, and such, it weighs 7200 lbs. with empty water tanks and puts 850 lbs on the tongue. I tow it with a 2012 Yukon XL Denali (6.2) and I'm within all weight limits, but only *just*. It's cammed and conservatively I estimate it puts out 450 hp and 460 ft. lbs. of torque. But that's not the limiting factor - there's plenty of power. The limiting factors are 1/ how much that trailer will wag the truck in windy conditions, 2/ keeping the engine and transmission cool in the summer heat, 3/ long-term durability with that kind of load.
As others have said, the short wheelbase will be an issue. The XL does okay with sway but I've pulled heavy trailers with 3/4 ton and 1 ton trucks before and there is a significant difference in overall stability. I definitely wouldn't want anything shorter. I also spent 2 weeks of experimenting to get the hitch set up correctly to properly distribute the weight and minimize sway. I've had to modify the cooling systems in mine to keep the temperatures under control (larger radiator, fan-assisted transmission cooler mounted below the bumper, one upgraded radiator fan motor of two, and an upgraded torque converter that won't eat itself when towing). Other guys I know towing similar weights have replaced their rear diffs 2-3 times, and our old solid rear axles are built hell-for-stout, usually lasting 300-400K without towing. TBD on the independent rear ends in the new ones.
Will the Duramax shorty pull it? Sure. All I'm saying is know what you're getting into and be prepared to get into a 3/4 ton at some point when you're tired of white-knuckle windy drives and throwing money into upgrades and repairs. These trucks just weren't engineered to pull that kind of duty for long.