I started out years ago towing our 7,000 lb trailer with my old chevy 2500 with the 350. I tow mostly in the Sierra and Rocky Mts. I hated the way I had to slow down to 45 mph going up the grades. So ...
I doubt it's a "problem" then the engine. Your engine computer would be lighting the "check engine" light if there was. More likely it's an issue with the rear-end, as in the wrong ratio. Do you know what it is?
With my ol trailer (about that weight) I had no problems with 60 mph on most grades. With the new (heavier) trailer (13,000) 60 can mean winding the engine to 4500 rpm (or higher)