Karl, here's the deal. Half the folks here will say you're fine and likely have done that much or worse with their trucks and / or understand a bit more than the published class/gvw rating. Then it boils down to how much you're willing to spend on mods to make it haul well and safe vs a turn key dually.
Others are strictly by the book and will allude to the killing a busload of orphans thing if you even try. Must all be Nationwide insurance agents or something......
The middle
Of the road answer is you CAN do it safely, But you'll need to equip the truck with a few things and you need to prepare that it will not handle nearly as well as a dually, and your comfort level for a big white whale humping your little truck will come into play! And that assuming your truck is good running and well maintained because you're using up most of its original capability.
Btw if it's a long bed, better than a short bed.
I've had the truck you have and I also haul a 4000lb. Camper on a short bed 3/4 ton currently.
I would, with your truck, knowing the axle rating, ditch the 16" wheels if you still have them in favor of 18 or 20" OE wheels (GM or Dodge) that you can easily get some 3700-4000lb tires for or for more confidence find some 19.5s.
Sway bar, make or buy some lower stable loads and add springs or air bags to suit.
With that, I'd be confident.