I've not yet driven this route but I have done some research on it because it's a trip I'm planning. Google Maps Street View has excellent views of the entire route, so you can check for yourself what you're facing.
The road is paved throughout its route, and with the opening of the Deh Cho Bridge over the Mackenzie River, the route can be driven all year long now (previously, a ferry and ice road were used, and there was a gap in accessibility in the spring when the ice road was too dangerous but the ferry could not yet run).
Note that there isn't solid mobile phone coverage on the route. It runs out in extreme northern Alberta and does come back with two or three cell sites of coverage along the NWT route. You may want a satellite phone. I imagine other drivers are pretty courteous about helping stranded drivers there, though. For the land-based cellular/mobile service, note that not all foreign providers may roam with the carriers in northern Canada, so check with your provider (wise even if you're Canadian) to see if your phone will work there.
As a ham radio operator I wondered if radio repeater coverage covered the entire route, but it too has gaps. There is coverage more or less from near Rae-Edzo up to Yellowknife and beyond. An amateur radio license will be required to use this service.
Note that in January, day length will be very short (you may only get five or so hours of daylight) and temperatures as low as -50 C and beyond are possible (-35 to -45 in January would not be at all uncommon there). Make sure your vehicle is in tip-top mechanical shape, and make sure you have an adequate emergency kit consisting at least of warm blankets, some high-calorie food, candles (for both light and more importantly, for warmth), water, flares (to summon help) and warning cones or triangles (in case you need to change a tire on the road).
There are few communities on the route once you get into far northern Alberta, so significant distances will separate you from communities at times. Plan accordingly.
Make sure someone knows your route and schedule, so that if you don't arrive on time, they will know to send help.
Best of luck and safe travels.