Your year range puts you in the realm of a mog that could have enough power and gearing (overdrive) to do the task.
That being said, I pretty much agree with Kurt. Unimogs, even newish ones weren't really designed for long distance on-road travel.
I love my mog (416 doka) for exploring and fairly rough offroading. I've driven it to the rubicon and back and to moab many times, but it was never too much fun on the highway.
The year range you are talking about would put you into a U1300 / U1700 / U2100 or other variant. They are all bigger and more comfortable than mine, but I suggest finding a way take a long drive in one to see what you are getting into.
I'm not sure how much research you have done. If you want to pm me, I can call or send you some info on recommended dealers, etc.