No you don't need a dually.
Did I say that????? :B
Run the figures through. From the figures you gave (1862 hitch, 11810 unloaded, 13860 gvwr) then it is mathematics that show this trailer is running 15 percent hitch weight ratio (1862 divided by 11810).
At that same ratio of 15% at gvwr of 13860 the pin weight would increase to 2079 pounds.
Your vehicle weighs 6900 pounds. Whats the gross weight rating on that year of Chevy, 9200 pounds????
Just for conversation, assuming it is 9200 pounds, then 9200 minus 6900 equals 2300 pounds of cargo carrying or hitch weight capacity left in the vehicle.
So you should be just dandy.
And honestly, you would really, REALLY, need to pack in the items to load that trailer up to its gross rating.
I would bet most times you use it you would be in the middle or say 12,500 - 12,900 pound range. That's giving you about 1,000 pounds of stuff, including water tanks, to pack into that fiver.
Shoot, even at 12,900 pounds (times 15%) the hitch weight would be 1,935 pounds. Well within the capacities of your current vehicle.
Go for it and enjoy.