This might be a little ambitious as a summer motorcycle trip (especially since 6000 miles is about two rear tire's worth, given the speed and terrain). One of the most interesting parts of that route is the Trans-Labrador Highway. Though it is the primary road across Labrador, it's still largely gravel and very remote.
My curiosity was piqued when Google Maps seemed resistant to plotting a route from Lodge Bay, NL to Québec, QC. Zooming in turned up this solitary road, and my next stop was ADVrider to see if anyone had ridden it and posted pictures. This guy had, and now I really want to go. Or at least I think I do. It's a long way away, especially on a dual-sport bike.
One interesting thing I found is that the Government of Newfoundland and Labrador has purchased satellite phones for free emergency use by travelers of the TLH. You can pick up a phone from any of several places along the highway, leave your credit card information, and drop it off again as you leave the highway. So there's really no reason to worry, Mom...