Not many pups require WD hitches, but can't say for sure without knowing more details on the trailer weights etc.
Could be a number of factors causing the bucking. A Taco should be able to handle a pup without problems. The distribution of the weight, especially on a single axle tt is very important to handling. I would check the tongue weight first. Too light on the tongue could cause bucking or if it's almost balanced front to back would cause it to seesaw. You want it to be tongue heavy, at least 12-15% of the trailer weight should be on the tongue.
Also consider the truck shocks. Are they old and worn out. Might want to upgrade to heavier duty and make sure the trailer and truck tires are aired up.