Payload is the real problem. 2011 F-150 7500 pound tow rating must mean 5.0L/3.55. Plenty of power and gearing. Bunk house means family and probably a crew cab. 1400-1500 pounds of payload gets eaten up quickly with 900 pounds of tongue weight and a family in the cab, before you even put camping gearing the bed.
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 2017 Subaru Outback 3.6R