You have a nice truck. It will do a good job towing that trailer. You will need a WDH. The brochure weights are always low, and normally don't even include propane or battery on the tongue weight.
I think you are also figuring low on your wt added to the trailer, but should not be a problem. I am thinking your loaded trailer will be closing in on 6,000 lbs, with tongue wt around 700.
Your truck should have enough power, and the 6-speed transmission will work great. You will know you are towing a heavy box down the road, especially in the wind. It should be a good experience, as far as towing goes.
Enjoy your new rig!
Jerry