You truck will haul a 4,000lb camper when prepped correctly and you won't die. I regularly haul my Arctic Fox 865 on my F-250 with zero issues.
I bought my F-250 with camper package and heavy duty everything, it is an F-350 in spite of the sticker. The part numbers for all the parts under it are the same as F-350 parts. Contrary to what the weight weirdos here will tell you. Ford and Mopar also, do not make different weaker parts with the same part numbers.
I did some upgrades, airbags of course, better shocks, Torklift bump stops to bring the helper springs in earlier, a stronger wheel and the best Michelin tire available. The truck already had sway bars. The only downside is that ride quality with no camper is a little rougher than before.
I've made several long adventures including two, three week, 5,000 mile plus trips with zero problems. My gross weight fully loaded on a Cat scale is right at max for an F-350.
When I buy my next truck, it will be configured the same way. Who knows, maybe I'll spend the extra $435 bucks for the F-350 emblem?