A 7,900 tow rating for an F150 suggests that it is not all that 'beefed' up a version of the F150 (that depends, somewhat, on model year, but many newer models go much higher than that).
With that in mind, your first place to look would be your hitch. It is highly possible that a class III hitch on a vehicle like that might have a weight carrying limit of 500 pounds (anything over requiring a WDH). Even travelling light, your trailer is likely to weigh as much as 5,500 pounds, and your hitch will likely be in the 600-800 range. How your truck will handle is questionable, but can only be determined by trying it out. If your hitch is limited to 500 pounds of direct weight, however, you are risking catastrophic failure by exceeding that significantly.
If your hitch is rated for it, you can try and see what happens if you want to. For me, however, I would not want to pull 1,200 miles with a set-up like that.