The trailer my mom, brother and I live in is a 40' long, 12' high fifth wheel, triple axle. The friend we got it from lives in Conroe and the trailer was in Splendora. He moved it from where he got it, to his shop and property, and then brought it to the RV park in SW Houston near 610. For all of this, he used a RAM dually one ton 4x4 with a Cummins in it. Our trailer weighs around what yours does, maybe a little more. I remember him mentioning 15K# in the discussion about getting and moving it.
That truck moved this trailer just fine. I've also seen him move loaded car hauler trailers with the Cummins powered dually he had before this one. He used to drive semi's and goes all over the South, buying and selling cars. So he's used to hauling heavy loads and knows what it takes to do the job.
My one ton crew cab would probably (if it had the appropriate hitch) move this trailer, but not near as well, and it probably wouldn't do it for a long distance. Certainly not near as well as a dually would. And unless it's an emergency I'm not going to haul way more than my truck will handle!
A few months ago, we went on a trip to Austin and back, to a big car show and swap meet. The truck had the 3 of us and gear for a long weekend in the back seat (including my tools which is 100# right there) and the bed was full of tables, parts and fixtures for my booth. We were towing a 5x8 enclosed utility trailer, that was full, probably 3600# total, trailer weight and contents. This combo would go all day on flat ground at 65; once we got into the hills it needed a little more throttle to keep that speed. The truck performed well on the trip, but I noticed that the extra weight did require a good bit of extra stopping distance. And this is a full floating axle, GM 14 bolt, 10.5" ring gear, with 13"x3.5" rear brakes and big discs up front. We weren't asking the truck to do anything it's not built to do, but even the small trailer we were pulling, would push you down the hill on a stop. Just basic physics there. Getting a large heavy mass moving takes some distance and effort; so does stopping it!
Last year at the park, a guy came in hauling a trailer almost as big as ours, with a '93 GMC one ton dually. He said it has a 454 in it, and he pulls this trailer a lot with this truck, and he'd just come from Florida with it. Only places he had trouble towing it was in the tunnels around Mobile, and I know those are steep grades. I bet the running gear isn't stock though! Didn't get a chance to find out more on this, because we were heading out of town, when we got home, he was gone.
There's often many newer 5th wheel and large bumper pull trailers here in the park; all are pulled by late model one tons, mostly duallies. A few of the 4500/5500 medium duty tow rigs too. These are just better designed for hauling the bigger trailers people use nowadays. When the squares were new, even when the OBS trucks were new, the trailers weren't as big, tall and heavy as they are now. It's not just about engines, transmissions, brakes and axles; the frames and suspension have to be stouter too.