I rode to Inuvik last year, was on the Dempster the last few days of August. Linky to my ride report.
I suggest DEFINITELY go in late August or very early September. That's the fall colors season in the Arctic, and it really is fantastic. You may hit some snow but just keep an eye on the forecast and treat the road with respect, IMHO.
Here's the sort of colors and fun you see that time of year on the Dempster:
This one from Top of the World Highway: