If your going by manufacturer specs on tongue weight you can't count on it being accurate. Usually the manufacturer seems to under rate the the TW. Maybe because they are not including propane bottles battery and a loaded trailer.
Your 12k hitch will be fine for getting your new trailer home. Once home you can do a little measuring. Without the trailer connected measure the distance from the top of your wheel wells front and rear to the ground (write it down) Now measure again with the trailer connected without the WDH (write it down) Now connect your WDH as you normally would and measure again (write it down) Now look at the numbers with the WDH. If your front was at 30" empty without the trailer 32" with the trailer but no WDH and now 30"to 31" with the WDH you are actually transferring some of that TW to the front of the truck. If you don't get any movement in that direction you either have to grab another link or go to a heavier WDH