I would plug your combination into U-Haul's selector, and if it rejects it, it's probably best to find another plan. Besides assuming all the liability in the event something goes wrong, there is some merit to ensuring the tow-vehicle weighs more than the the auto-trailer once its loaded, since you can't use weight distribution.
Plus, it's unlikely the current owner of the van has installed a Class-5 hitch. It just doesn't make sense to put one on a van with a small motor. And that loaded auto-hauler will be well over the 5k rating of the stock hitch receiver (that's the non-weight-distributing limit).
