The published dry weight is not the actual dry weight, check the sticker on the trailer when you go back to buy. Also as mentioned earlier look at the hitch on the truck it will have a sticker on it with the allowable tongue weights with and without a WDH.
The truck will have no problems pulling the trailer but you will more than likely be over your cargo capacity (or at least right at it) depending on what else you put in the back of the truck.
Purchase a good WDH and don't depend on the dealer to set it up properly, you will have to do that yourself. Take a trip to a CAT scale and will be able to get it dialed in.