Not enough truck in at least two areas.
Payload: 2152 - 150 pound 5th wheel receiver - 1860 = 142 pounds for you, your wife, anything else in the truck and anything in front of the RV axles.
Tow ratings for 2007.5+ GM 6.0L/6-spd/3.73 is more like 9.500-10.5k pounds, depending on cab, bed...