"You will likely be really close to that 12,500 pounds."
Let's not overlook the tongue weight that a 12,500# {assuming you can keep it to that} will generate. Tongue weight should be around 13 percent of the loaded weight of the trailer so you will have approximately 1,600+ # and then add another 100# for the weight of the WDH.
Now you are at 1,700#+ that comes right off of your trucks payload and this is before you load anything or anyone into the truck. Even if your truck has 2,000# of payload, and most do not until you start looking at 3/4 - 1 ton models, you can only load 300# of people and gear {which is not much} without being over. Now check your max rear axle weight rating and do not be surprised if you are well over it... :E
Anyone who quotes you "Dry" weights is not your friend. :S