Based on the truck and trailer in your profile I would say not required assuming you meet hitch tongue weights provided by your truck which I think you do if they are similar to Ford 3/4 tons.
I towed my 7k loaded trailer about that distance with an F250 without issues. It met the hitch loading and weight specs without the WDH and was stable. At the time I had no sleeve to adapt to the larger reciever for my WDH but I did have a ball that met the specs.
That said I have an F350 now and use my WDH all the time.
I wouldn't think twice about not using it. I had to pull my 25' toy hauler over 500 miles when I first purchased it, and I was worried about this same thing. Especially with a GMC 1500. The tongue weight was around 900#.
I called a friend who worked at an RV place to get his take, he laughed at me. He told me how the dealer he works for pulls travel trailers a whole lot bigger back and forth to RV shows and they never bother switching the WDH's between trailers. I grew up on a ranch, and he reminded me how we pulled stock trailers full of cattle all over the place, without even thinking of weight distribution.
My toy hauler pulled great those 500 miles! So great I contemplated never getting a WDH, but I did since this unit will be doing a whole lot of traveling in the future.
You will be fine. Very fine. Especially with the truck you are using.