Just going with a typical options + provisions + your stuff trailer weight "bloat" you're looking at a trailer that weighs around 8000lbs loaded and ready to camp. Tongue weight will be a minimum of 1000lbs, and I would not be surprised if it's around 1200lbs.
That's borderline for ANY F150, except for the 7-lug HD payload package version. If you carry much in the way of people and/or stuff in the truck, odds are you are overloaded.
Hopefully I'm erring a bit to the heavy side here for my armchair quarterbacking. You will definitely want to get it weighed to get a clear picture.