Ooooodles of suitable units available, some on the shelf at a parts store near you. Pulley can be swapped with hand tools, local auto electric shop can also rebuild.
In the interest of further diagnosis one can also "bench" test alt on the vehicle if you manually supply voltage to IG and S terminals on alt side, while monitoring voltage at big stud or battery if confident that path is ok.
Back to that plug though....
Ok, 98 percent you need an alt, but lets verify shall we. Easy check is 'charge' or 'alt' fuse, may be in underhood box, may be in box in cab near your knee when seated.
If i recall alt is 3 wire plug, one is keyed power (says hey wake up), one is 'sense' voltage (determines how much to charge...
Dont overthink it, this vehicle doesnt rely on an ecm to control alternator. Once again, I've seen this before, twice. Both caused by lack of charging. Did you tap alternator with vehicle running?
Yep your dash voltmeter and big red charge light tells me the same, why all the rest come on I can't say but I've seen it on two other hdj81's. Can give alt a tappytaptap as well with vehicle running.
Give alternator plug a wiggle, unplug and plug it back in. While your under the hood make sure belts are present decent and tensioned. Have seen this before fear not.