I have an 08 Yukon Denali. GM intro the 6 speed in 08 on Denali. 6.2 L rated at 7900 lb towing. I pull a 31 ft Apex Ulta Light...dry at 5400lbs, est loaded at 6200 lbs. WDH and sway control. I frequent the NC mountains with no problem. Always use tow haul when towing. My only drawback is SWB and payload at about 1350. I pull out the 3rd row seating and travel light. Considering upgrade to a pick up that has a longer wheel base and more payload...based on our desire to go cross country.
You are good to go if vehicle is well maintained, dialed in for towing and don't exceed payload. Happy Trails!