Weight wise, At your payload of 1969 and 625 worth of family/payload, I think you will be OK as long as you don't overload things and probably don't tow wet. My hunch is your going to be under 1000 lbs tongue weight fairly well loaded. Do remember, toppers, spray in liners, anything added after the manufacture of the vehicle will count as well.
If you want to firm this up, you could take your vehicle loaded to a scale, weigh it. Your available tongue weight should be pretty much the GVWR of the vehicle minus your gross vehicle weight. Don't forget a few hundred pounds for your weight distribution hitch. Also, the tongue weights on the specs generally don't include a battery or gas bottles.
WORST CASE, as long as you don't exceed the GVWR of the trailer (2017 model is GVWR is 9250) at 15% tongue weight (which is probably the max you want anyway) your only at 1388lbs. I don't think you will ever get that heavy if you meter your loading a little and keep stuff out of the bed. You can get fairly inexpensive tongue scales off Amazon and I would think the dealer would let you set the trailer on the tongue. They probably wont let you load it up and take it to a scale unfortunately :-)
If you havent, use others cat scale results, this one is a good example http://www.jaycoowners.com/forums/f3...hbe-37715.html
Kudos to you for looking into this ahead of time, I wish I had looked into it more.
One more suggestion on the F150 if your going to be near payload, look at rear suspension enhancements. I used the Roadmaster Active suspension, many use the timbrens and/or shock upgrades. The R.A.S made a world of difference when we used to tow with our F150.