Welcome to the forum!
Well, honest opinion from someone who has been towing lots of trailers for lots of decades, as good as the F150 is, for a trailer of that size and weight, it is simply not enough truck.
Minimum F250 with a decent size engine is what I would go with. Consider more than just getting the thing moving. 3.6 is way too small, even though they do amazing things with power from a small engine. Even the 5.0 is going to struggle on hills and such.
Also consider the suspension etc of the F150. Great ride, but springs and other components are softer than an F250, and therefore more prone to sway.
Sure you can doll it up with extra goodies to help tow better, but at the end of the day you really are better off with a minimum F250 with either a diesel or bigger V8 gas. You want lots of torque to pull in comfort.