Guess ill buck the trend here Mike and say that you can haul it relatively safely with the right mods. Coming from a guy with a 4klb plus camper on a 2500 that has logged the Alcan hwy and a bunch of AK back roads without issue.
If your F150 is the 7700? Lb gvw with the goofy 7 lug rims then you are in pretty good shape. They have a heavier rear diff than the std 150s.
Either way, tires are a must. Good OE alloy wheels or steelies. No foofy dubs on it.
Sway bar highly reccomended and then your favorite flavor of suspension mods. Timbrens will do it, add a leafs or airbags.
FWIW, my old '11 F150 made its first 40k mi with the OE C rated tires hauling a constant 800-1000lb in the bed, pulling a 14k deck over trailer with some substantial tongue weights with just timbrens. Truck is no worse for the wear. Just saw it yesterday, 60k and climbing. Not ideal but that's what happens when the district mgr doesn't think you need a HD truck.