Just as a reference, I tow a Fun Finder Xtra XT-245 toy hauler, a similarly sized toy hauler.
5025# yellow sticker empty weight,
6740# loaded with two dirt bikes and gear, but no water or generators.
The factory spec hitch weight was 765#, but with the WD hitch, it added 720# to the GVW of the truck. That put it 180# under the GVWR of the truck, 98% of rated capacity, with two people and some luggage in it. It added 880# to the rear axle, putting it 50# under limit, 99% of capacity. I need to crank up the WD to get a little more shifted from the rear axle to the front axle.
You didn't list what your truck weighs loaded with people and gear. I would think you would need at least 720# of payload remaining after you load your truck before you hook up a similar trailer.
My Ecoboost is rated for a GCVWR of 15,300 and the rig weighs 12,920, about 84% of rated capacity. The engine pulls it with no sweat, but the rear suspension rides quite stiffly.