Not enough truck! You should be looking at a 3500 dually. Forget dry weight, nobody pulls an empty trailer. Your maximum wet weight is 16750, 20% of that, 3350, is on the hitch if fully loaded ready to go. Now add the weight of hitch, passengers, dog, and anything else you carry in the truck to determine your payload which had better be less than the rating on the yellow door sticker.
The salesperson wants the sale and will tell you what you want to hear, once you leave the lot you are on your own. He/she may have little or no experience towing so good that you are doing your homework here.