Look at the driver side door post there should be a sticker there which gives you some info. Primarily the payload capacity. Is that the empty weight of the trailer or the max weight. If it is the empty weight the actual weight will be more like 10,000# and the tongue weight will be around 1500#. Take the payload number subtract the weights of all passengers, dog, luggage, ice chest, misc stuff and a weight distributing hitch from that payload what is left over must be greater than the tongue weight.
As for the F150 the answer is maybe, it has to be setup with the right accessories, the max towing package and 17 inch tires. Even then I'm not sure if that would be enough.
Arctic Fox 25Y Travel Trailer
2018 RAM 2500 6.7L 4WD shortbed
Straightline dual cam hitch
400W Solar with Victron controller
Superbumper