one, as mentioned weigh the system and see what your actual tongue weight is
next what is the weight carrying limit on the hitch?? Often it is a LOT less than the weight distributing capacity.
you could easily have a tongue weight near 1000lbs. remember the "empty" tongue weight is w/o any battery(s) with empty propane tanks, and nothing else in the trailer. And the battery(s) and propane basically transfer 100% of their weight to the tongue since they are so close.
Now if you are within the weight carrying rating on the hitch then it's possible to consider no wd hitch. But it is also possible that the truck will handle much better with a WD hitch putting the front axle weight back to it's unloaded weight.