Rear Living, just a couple in the cab? The dry hitch weight is high and will go up, so you need something with about 1200 pounds of receiver rating. Need the max trailer towing package or HD payload package.
The engine/trans are plenty for that kind of weight.
A & A parents of DD 2005, DS1 2007, DS2 2009 2011 Suburban 2500 6.0L 3.73 pulling 2011 Heartland North Trail 28BRS 2012 VW Passat TDI