I live in NC but the rules are mostly the same everywhere. The licenseing you need is based on GVWR. If your trailer is over 10k+1 you need a CDL. But keep in mind(at least here in NC)you have to buy enough weight rating when you buy your license plates as well to haul a given amount of weight.
I have my F-350 licensed for 24k because I pull a gooseneck or a dump trailer or a tilt deck,all 7 ton. I have to account for the weight of the truck,trailer and the load and not go over my limit.
On my F-750 I'm licensed for 45k so I can haul 8 tons,plus my trailer(10 ton) and a machine.
I have a class A CDL