Sorry if this sounds angry, but based on a few of your comments I want to make sure you're aware of where this highway is.

Whatever you end up taking, keep in mind there's quite literally no services between the Dempster turn off (40km South of Dawson) and Eagle Plains, so whatever you drive, make sure you have the fuel and supplies you need. No gas, no stores, no hotels until Eagle Plains.

NO cell coverage on the Dempster. I don't mean "oh the coverage is spotty" or "you can only get 3G". I mean quite literally, there is zero cell coverage on that highway.

Sat. phone might be worth the piece of mind for you or those at home. There are also no emergency services on the Dempster. You're more or less on your own in an emergency situation.

If you break down, AND are able to make it back to a phone AND find a tow truck willing to make the drive up the Dempster, you're looking at the most insane tow bill you can imagine ($1000 would be quite easy to reach, depending on distance and vehicle towed)

It's probably the most desolate drive you can imagine. Frequently closed at Rock River due to blizzard. When closed, the highway could be closed a few hours up to a few days.

Keep in mind that the "Dempster highway" weather forecasts cover an extremely limited area of the Dempster highway, and may not always be accurate outside of that area.

Unless you're familiar with winter driving in remote areas, or have a reason you have to be in Inuvik or Fort McPherson or something, I'd suggest you do the trip in the summer, or find another Yukon winter destination.

And like others mentioned, check with the rental agency to ensure the vehicle is allowed to be driven on the Dempster, they often aren't. If you choose to ignore this and drive on the Dempster anyways, then I imagine you'd be uninsured and responsible for any damages.

If that all sounds fine, then I'd still suggest a 4x4 over 2wd w/chains.