I know it is not exactly the same, but I tow a 7000 pound boat with a 2011 Yukon Denali XL.
Some of the issues I have (like trailer sway) shouldn't effect you. It has OK pulling power, but don't expect it to stay in 6th gear. Mine is in 5th most of the time, and will drop lower when it hits a hill.
Going through he mountains of Colorado, I see both engines and transmission temps approaching 250*. Two GM dealers and an independent transmission shop all told me that is par for the course towing heavier through the hills.
When we replace our Yukon in the next couple of years it will likely be with a new style Navigator or Expedition. I believe they have higher towing capacity.