Even 12V is a weight cop now? Lol
OP, here’s the short list of why your truck is fine, or isn’t fine for that weight. Although how and where you tow also plays into it. (Namely pulling big grades in the mountains or just across flatlandistan with no nasty headwind.)
Assuming truck is in top overall mechanical condition.
Chassis in general, zero issues. Hell, I drag 14k bumper pull flatbeds up n down the cascades with a half ton, reliably.
Engine, zero issue except low on power by todays standards. Doesn’t give up anything in practical application to a 6.7. Actually it’s the other way around unless you delete the 6.7. That is easily fixed for about $500 plug n play some mild tunes. And an exhaust brake is a major luxury, I’d say an almost necessity in the mountains.
Transmission? That’s the issue. If you have a 6speed with a good clutch in it, no issues there. Hook n book.
If it’s an auto, it’s the single largest drawback of the early 3rd gens, period.
A 1980s era 4 speed with too tall of first gear and not enough gear splits is half the problem. The other half is that, unless you have it built right, it is likely not up to the task of those kind of loads, for very long. Again that’s less of an issue in Kansas with a tailwind. And a huge issue going over the Rockies or any other big grades, especially in the dead of summer.
Bottom line, auto w built trans, I’d do it, begrudgingly. 6 speed, I’d be east bound n down without a care in the world.