You need to figure out the weight of the camper including water, propane, food, clothes, people, dogs, etc. The manufacturer should be able to provide the camper "wet weight" - and then you have to figure personal items, food, etc.
Size the truck to fit the load. With the camper you've described, I'd get a dually based on my experience with two different campers. I have had a Bigfoot 1500 and a single rear wheel truck (F350, crew cab) and it handled the weight with no problem.
After about 10 years I moved up to a Bigfoot 2500, 10.6 which is about the size of the camper you're getting. The SRW did not handle the weight comfortably. There was a lot of side-to-side rocking of the vehicle in certain conditions. I sold the truck and got a dually, F350 crew cab and the camper has been on three different F350 crew cab dually trucks.
I prefer diesels and all of my truck have been diesels. The reason is not the weight, but the wind resistance of the camper at highway speeds. Going into a strong headwind (20+ mph), I can see the fuel mileage drop 2-3 miles per gallon - that's how much of a load the wind can make on the entire rig.
I travel the western states and if you couple the headwind with going uphill it's actually quite a load on the vehicle. The diesel handles the load with no strain making the driving experience much better. No down shifting, no high motor revving, etc. The motor just hauls the load uphill with a headwind without laboring in any way. I like that.
As for manufacturers, you need to ask if the manufacturer has a "camper package." Some manufacturers do and it adds sway bars, different shocks, automatic power disconnects to the vehicle battery and a few other items. The vehicle is also certified by the manufacturer for camper usage.
One thing you may want to take into account is that the 7.3 liter Ford gas motor will only be available with a 4:30 rear end when it is introduced. Depending upon the 10-speed transmission's gearing, that may make for high revs at highway speeds. But, since no one has tested the truck with the 7.3, and the reviewers that currently have the trucks to drive only have them with the understanding that they will make no comments on the driving experience until January 2020 when the truck is officially released. So, no one knows the truck's performance with that motor, RPM at highway speed, etc.
As a contrast, I have a 3:55 rear end and a six speed transmission with my diesel and that puts the engine RPM at 1850 at 75 MPH which is about 200 RPM above where the torque plateau starts on that motor. Because it's making lots of torque it rarely downshifts going uphill.
I would also suggest getting air bags regardless of whether you have SRW or dually. They don't increase the load carrying capacity but they come in extremely handy to level the truck once the camper is loaded.
You can also use the air bags to level the truck front-to-back when parked and also side-to-side if you get a system with individually controlled air bags.
I also use the air bags to make loading and unloading the camper easier. As an example, I raise the camper to give me clearance above the truck bed with the air bags at 5 psi. I back the truck under the camper and then inflate the air bags to 75 psi - that puts the bed of the truck in light contact with the camper. I then only have to drop the camper down about 3-inches to get it seated on the truck bed.
I do the reverse when taking the camper off. I inflate the air bags to 75 psi, extend the jacks down to the ground with no weight on them, then raise the camper about 1-2 inches, drop the airbags to 5 psi which gives me about 3-inches of clearance, and drive out from under the camper.
Have fun with shopping for a new truck and enjoy the camper.