I think it would work. That said I'd advise also going out and driving some F150s. With a crew cab and canopy it would compare favorably to most SUVs, it wouldn't cost any more and it would give you the flexibility of potentially upgrading the trailer a bit down the road and not having to factor in the weight of a bag of potato chips you want to bring along. Just something to chew on - changing tow vehicles is expensive.
We towed a pop up for years with a Pilot with less power and it worked okay, so I do think you can tow successfully with a unibody FWD biased platform. I just like pickups more.