I have a Keystone Cougar 316 RLS, according to the brochure:
Dry - 10,436
Gross - 12,300
Hitch - 1,900
Last time I went over a scale (this june on a 4000 mile trip) the hitch weight was 2,500 and there was very little in the basement.
I will tell you that with my 2016 F250 there was absolutely nothing else in the bed and it was me, my wife, teenage daughter and a 40 lb dog in the cab. I had cleaned everything unnecessary out of the truck to try and save weight. I was under on the individual axle weights, but 800 pounds over my 10,000 GVWR.
The 6.7 in the truck pulled that trailer like a dream even through the mountains in Yellowstone and Colorado, However, not once did we run into bad weather or have to panic stop.
Though you will probably get plenty of people telling you that you will be fine, you might want to consider going to a 350.
I would rather have excess capacity, would like to actually put some stuff in the bed of the truck, and live in an area of the country where DRW is not much of a hinderance - I have a 8/16 build week for a 450. Also means when my wife wants a bigger fiver I don't have to get another new truck.