I pulled a similarly-sized trailer all over the country with my '01 half-ton Burb, including the Rockies.
I'm guessing from that floorplan that it's just you and your spouse? In other words, no other family members to eat up your payload?
Yes, you'll be pretty close to the limits, but that 6.2 should pull fine.
2008 Suburban 2500 3LT 3.73 4X4 "The Beast"
2013 Springdale 303BHS, 8620 lbs
2009 GMC Sierra 1500 Denali (backup TV, hot rod)
2016 Jeep JKU Sahara in Tank, 3.23 (hers)
2010 Jeep JKU Sahara in Mango Tango PC, 3.73 (his)