Yukons are Tough
You should be fine. I pull a 24RKS at 4900lbs dry with a 2001 Yukon with a 5.3L. My tranny temp hit a high of 205 degrees. Now for the good part. The elevation started at about 5,000 ft and ended at 9,500 feet. 5-9% grade. I kept the speed down to less than 25 MPH.
I wish I had the longer wheel base and newer technology but if you are patient, what you have will work fine. Just don't push it and make sure you have the towing package. Max weight is 8,000lbs plus. Check at the dealer service center if you have to so you know what you have.