There's really only one bike to do any trip on, be it gravel, dirt, paved or what not.
A Harley any Model!!!!

 

A rental.

 

I just did this this summer on a Road Glide. Traveling with me were 2 EG's, and a Road King. We saw a good number of sport touring bikes along the way, plenty of standard HD's including sportsters, but the Sport Bikes were very rare. I think we only saw 2.

We went up the Cassier and back the Alcan. No problems, and you should worry about tires other than normal wear.

 

I've done 3 round trips and 2 one-ways (shipped) on my 97 dyna wide glide. Only breakdown was near Cache Creek and met some great folks along the way. Fill up when you get the chance and have a great time. Kluane Lake, where they appear to be working on a lifetime vesting program for construction workers, was the only problem area construction-wise this past summer. The last 100 miles in Canada north-bound are a bit, Frost-Heaveish. Enjoy it on anything with a 125 mile fuel-radius.

 

This is on my bucket list. And I'll do it with whatever bike I own at the time. Although I like the idea of the rental.... Significantly less damage potential to my scoot.