I towed my Starcraft 18SB for a couple years with my 2012 AWD Traverse.
While my trailer is about a 800lbs lighter, it has more tongue weight than the 19H. If I had to guess, my tongue weight is well over 500lbs, but I believe my Traverse had around 1500lbs of payload.
After towing a couple times I made the determination that I didn't need a WDH. The trailer only dropped the rear of the Traverse about 1- 1 1/2 inches at most, even with the wife, two kids (small) and gear in the back. It towed bullet straight even when passing or being passed by other trailers on the highway. Never once did it feel unsafe.
The high final drive on the Traverse made it feel a tad light on power at 65mph on our hilly highways here in VT. It performed much better on secondary roads up to 55mph where I would hardly know the trailer was even there.