Time for Deh Cho Trail trip
I'm sorry I can't offer you advice on this particular trip, having never driven north of Kamloops. I can tell you that we generally recommend that people drive no more than about 500-550 miles per day. But this recommendation is generally for the United States, and usually interstate driving or a mix of 2-lane/interstate.
If you were able to maintain this rate of driving, your trip would take roughly 18 days. However, if you traveled at this rate the whole trip, you wouldn't have much time to stop and explore anything along the way as 500-550 miles usually translates to about 10-11 hours on the road once short stops for food/fuel/bio breaks are factored in plus occasional traffic congestion/road construction. But, where you're going, I know that it will take several more hours daily to maintain that pace.
Also, we would never recommend that someone maintain that pace for so many days. First, you're missing the exploring part of the roadtrip. Second, you will get tired of driving this much and need a break by either not driving for a day to rest up from the road, or at least having a few driving days interspersed throughout your trip, where you drive far less miles (may only 100 or 200 at most).
I was doing some playing around and came up with this. It shaves about 1500 miles from your trip and that will probably make a huge difference. Maybe save the Vancouver BC/Seattle WA stops for another trip.
However, I do agree that you might also enjoy taking the ferry south. You could do something like this. Of course, you would take out the leg from Prince Rupert (D) to Bellingham (E) saving you 900 miles for about 7400 miles.
If you decide to do this, you will need to check sailing schedules pronto and get your reservation paid for. These trips can fill up fast.
I have always wanted to drive to Yellowknife myself for some reason. But I think I need more clearance than my New Beetle has. :)
I wish I could be more specific help but I hope this has given you some information to weigh in your decision.