Our 2011 3500HD SRW duramax.
Towing - 10 to 12.5 pmg (55 to 65 mph). Slower speed - better mileage.
Not towing - 22 to 18 mpg highway (55 to 70 mph) Slower speed - better mileage.
Took a trip out west (Yellowstone/Glacier) this summer and the trip average was 10.7 mpg.
Like others have said for a 13,000 lb fifth wheel you'll need a 3500HD and depending upon the pin weight a dually.
3500HD SRW - GVWR is 11,600 lbs with the diesel. 2500HD GVWR is 10,000 lbs with the diesel.
Not sure where you live --- in New York state if the combined GVWR of the truck and trailer exceeds 26,000 a class R license is needed - another road test towing the fifth wheel with the truck (city, highway and parking)