The 1200# payload is probably optimistic as well anything you add to the truck after it rolls off the assembly line eats into available payload.
Last two trucks I have purchased had undercoating and Line-X applied at the dealer and within a week or two had a toneau cover installed and by the time I got to the scale to see my actual payload I was down a couple hundred pounds already.
I had a 2013 F150 with ~1400lbs payload and a lighter trailer 281BHS. I crunched all the numbers before buying the trailer and knew it would be close. The first time we hit the scales with my wife and two children under 3 we were within 32lbs of the rear axle rating. I would say the truck did fine but it was not a pleasant, relaxing drive.
We now own a F250 and life is good!
2014 Jayco Swift 281BHS
2015 F250 XLT 4x4 Crew Cab, Short box, 6.2 gas
Solar powered! The trailer not the truck!