Upvote:1
Neglecting the fact that collecting Qatar miles may not be your best option to fly with Qatar/OneWorld, the best option you have, living in Canada, is probably to collect Starpoints (from Starwood Preferred Guest loyalty progam)
Starpoints can be transferred at 20k:25k (1:1.25) to Qatar, and there are options in Canada to acquire Starpoints without actually staying with SPG.
(Canadian) SPG credit card typically has a sign-up bonus of 20-25k Starpoints, and the Membership Rewards points earning cards has a larger range, around 25-50k MR points.
Upvote:3
You could stay a lot of nights at one of any number of hotels and/or rent cars similarly.
For credit cards, your only option that I can find is the RBC British Airways Visa Infinite which has points that can be redeemed for flights on oneworld airlines. Alternatively you could use an American Express to generate points and then purchase the flight through their travel planners using points.
Looking through Qatar's bank partners there's no options listed for Canadian residents as most are based in Qatar/the Middle East, Southern Asia (India and Sri Lanka) or the U.S.