So, took the Dodge Cummins 3500 and the weight distribution system I got and hooked up my trailer to it to go get the hitch system installed. The hitch expert took one look at my trailer and truck together and said I didn't need the weight distribution. In fact, the truck could have been lower with more weight and be fine. It sat very nicely on that 1 ton truck. I sold the weight distribution hitch. While pulling the trailer I noticed it pulled just fine with absolutely no sway. The way the trailer is built and where the axles are it looks like I wont need a system now with the 1 ton.
The trailer's previous owner pulled it with a 3/4 ton and just on the ball hitch with no system, and he had no problems at all. So I'm thinking I will be fine with the 1 ton as is with this trailer.