I pull an 18k# gooseneck horse trailer with a dually. I'm 400# over truck's GVWR, 3,000# over GCWR but 300# under axle rating. Completely legal and as you can tell bt that not a member of the weight police.
That is too much trailer for that truck. The trailer lightly loaded will have greater than your stated 3k# limit and that doesn't include your hitch, passengers and stuff in the truck so I suspect it might even be over your axle ratings which would make it illegal. You need to be looking for a FW that has a GVWR of less than 14k# and preferably less than 12k#