The 1030 on that truck will be fine.
My truck is a 1996 dually and my camper seems to be of similar size. Although, the above weight estimate seems high. That poster may know for sure if he's had one. I estimate mine at around 4000-4500lbs. Really should scale it, I know!
Truck only has airbags. But stock it came with overload springs. I'm a truck guy, so I wouldn't be okay with anyone but myself hauling anything with my truck. But that's solely up to you. Take a look at your truck and see if it has overload springs in the rear and a sway bar. I remember looking at a '96 12 valve that just happened to not come with the overload spring option. When I haul my camper with my dodge, which also doesn't have overload springs, there seems to be a notable difference. Like having to use 80psi in the bags versus only 35-45 psi in the bags on my dually. Not cool to me because when you go around a corner and the camper leans, all the pressure is going onto that bag with no spring there to help it a little.
The truck will handle the camper. But it will be able to be felt on there for sure.
If your truck has a rear away bar and overloads, it'll make things easier with a camper. If not, then it's doable, but I would really recommend adding a sway bar. Sounds like something that shouldn't even be mentioned. But as I said, my dodge didn't have either. And even though it's only a 2500, I also looked at a couple of one-ton 3500 trucks and I know one of them didn't have overloads for sure. That kind of steered me off because it didn't seem like the truck was ordered and optioned for heavy hauling. As I had to spend more money after I bought the truck to set things up and tow my boat, I wanted to get a one ton truck that already had the suspension stuff done, and if I felt I needed, then I could upgrade with a bigger sway bar or the torklift overload things later if I felt I needed them.