Your truck will pull a 6000lb TT just fine. You won't win any races uphill. You won't use 5th gear much or 6th gear at all unless going downhill. The chassis and components will handle it admirably.
My current work truck is identical to yours except it has 3.42s....I think? At sea level, it'll pull a 14klb flatbed to over freeway speeds before it's time to merge into traffic. 2 days ago, I pulled a 28' flatbed deckover weighing about the same or a little more than the camper you're talking about over 3 mtn passes in the Cascades and noone passed me because I was a slow moving vehicle.
Your gearing isn't ideal (unless I happen to have 3.08s too).
Trailer brakes and a wdh and leter rip!
