Towing a Travel Trailer

I think you'll be fine. While new trailers are often heavier than their shipping weight clams, they'er certainly not at their GVWR. I don't see anywhere where you'll be beyond anythings specs.

I would verify payload on the driver's door Tire and Loading sticker. I haven't seen any 2009+ Rams with actual payload that high.

Otherwise, you should be okay as long as payload is correct and you won't load too much into the cab and truck bed. Get a WDH with integrated sway control.

That TT has a GVWR of 8600 making tongue weight well over 1K, payload will more than likely be exceeded. At over 32' you will definitely need a high quality WD/SC hitch that is properly installed and correctly dialed in. I would guess your 2013 Ram could pull it, but the towing experience will not be an ideal one to say the least.