Hawkeye02, the simple answer is YES. The truck will pull the camper alright.
The tough part is what is your definition of alright. If alright means there are no immediate breakdowns and the truck can physically move the trailer down the interstate, then you are good to go.
My definition of alright and most other folks is quite a bit different. I want my trucks gross weight and payload to be as much as practical to better fight any sway that may occur. I also want enough HP, torque and transmission to keep me locked up in overdrive to: Keep me and my family up to Interstate speed more often and prevent premature wear of internal components and just generally enjoy the trip to and from a WHOLE LOT MORE than the white knuckle driving an underpowered gasser may create.
My Chevy is built for towing. It's got heavy duty chassis and springs, 4 wheel disc, a huge MODIFIED 6.0 liter gas engine and a specialized option on the transmission that changes shift points and lockup settings. IT BARELY CUTS THE MUSTARD and I'm certain will be worn plum out in a couple years.
Theres loads of folks that will tell you otherwise and loads of folks that have done it because just good enough is enough for them.
My 5.9L Cummins 12 valve has 324K carefree miles of pulling 7,000lbs+ while getting better fuel mileage and always staying at Interstate speeds. Thats my version of good enough. I'm simply not a fan of using gas for towing.
Just my $.02
I hope this helps.