From what I read, the Toureg TDI has a tow rating of 7700 lbs. That's sounds marginal to me if the dry trailer weight is 4700. Remember that the tow rating does not include any gear load in the tow vehicle - it's just driver and passenger at 154 lb each. And the Toureg also has to carry 10%-12% of the gross trailer weight as hitch (tongue) weight. That too is probably within the Touregs load limit, but up near the top end of it. On general principle I'm leery of any car or SUV handling when its weight limits are being pushed.
Reports are that the Toureg is an excellent tow vehicle when compared to other SUvs, but that's not the same as your 1500HD. If it's the diesel you want, there are half-ton diesel pickups available now. F150, Colorado, Silverado/Sierra, Ram,