hauling capability

Simplest answer is to weigh your truck, and subtract that from your GVWR.

If your truck is close to stock weight, you can go by the sticker on your door. There should be one tailored to your specific build, specifying weight capacity.

also there may be a sticker in the glovebox listing max camper weight.

Just don't listen to a camper sales guy, cuz his answer will be "your truck will handle this no problem"

I called customer service at Dodge. Gave them the VIN and they gave me the payload figure for the truck I had. I then chose my truck camper. Worked out very good.

In 2015 there should be a yellow sticker on the driver's door post stating the payload capacity of the truck as built.

The reality is, folks usually have a hard time finding what they want and staying within the truck's "rated" hauling capability. Seems no matter how big of a truck they have, they always fall in love with the bigger camper.

This is where you start picking and choosing which ratings to acknowledge and which to ignore. First one to ignore is GVWR. If you read further on your truck's weight ratings sticker(s) there will be ratings for each axle with a certain size tire at a certain PSI. Those combined front and rear axle ratings usually add up to around 2000lbs more than the GVWR of the truck in a 350/3500 SRW.

2015 Fleet Ford spec show a F350 srw crew cab 6.2 engine can have over a dozen gvwrs ranging from 10000 up to 11300 lbs every 200 lb increments or so.
Also shows a 6290 or 6730 or 7000 rawr ...all above depends on 156" or 172" wheel base and 2wd vs 4wd and 17" vs 18"/20" wheels.

Every trucker should know his trucks front and rear scaled unladin axle weights. Drop by a set of CAT scale and find your trucks axle weights with attention to the rear axle as its going to carry most if not all of a truck camper weight.
Simply subtract your trucks rawr from scaled rear axle weight = the truck actual payload.
Also works the same for the front axle . Gotta' know your vehicles loaded axle weights. You sure don't want to exceed a tire/wheel or spring pack ratings.

Good grief…the factory rated payload is on the door sticker.
However you won’t like what you see. (And if it has a lower optional gvwr rating and correspondingly lower payload, know that that is very false and use your configuration at max option gvwr and add the difference to your rated payload for an accurate max yet somewhat conservative payload.
Although payload will be be better with the gasser under the hood (even though that has virtually zero real world effect on rear axle payload which is 98% of the equation for a TC).
The fact that it’s an original chassis Super duty makes it a little twisty-er than any GM or Ram from the mid 2000s up. But it’s not weaker.
Stick to sub 3500lb empty TCs and plan on beefing up the suspension a bit and you’ll be ok in the 4k range up to about 4500lbs tops. Any more than that and you’re blowing out of the tire/rim ratings by somewhere between a little (which doesn’t bother me) and a lot, without going to Method wheels and big tires or 19.5s (an option in conjunction with good suspension enhancements).

And you can bank on your empty rear axle load being about 3klbs maybe a few hundred lbs more, tops.
Can get a scale weight to prove it to yourself but it’ll be in the 3k range.

Open Driver's door, locate this sticker, note what your number says where this picture shows 1579. For dry truck camper weight, I recommend recommend at least 1000 pound under, but closer to 1500 pounds. The sticker on your truck will include anything in the bed and cabin. I expect someone will be driving that has weight, anyone or anything else inside, plus your typical camping gear in the cabin or in the TC.

And OP, if you ever come back to this thread, take time to digest what I told you. Many people don’t understand it, as evidenced by some of the posts here and the cacophony of personal theories about cargo weight that pop up every time this fairly redundant question is answered.

As stated weigh both axels independently at CAT scales with at least a half tank or more of fuel on empty truck.

The rear axel will carry nearly all the load of a truck camper. >90%. If you have a dually you can carry just about anything. SRW config your limit will be the tire rating X2 for the rear axel.

Example: for my 98 Dodge 2500 Rear axel empty no tailgate is 2540lbs Tires are rated 3042 at 80 lbs. So max weight on rear axel not to exceed 6084. Axel is rated at 7000 so the tires are the limiting factor.

I weighed the truck again with camper loaded and rear axel was 5840. Good tires are a must and inflated properly. I run 80 in the rear and 50 in the front. Air bags can be used to level truck if needed. Advisable not to tailgate either! My truck is 25 years old and not broken yet!