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The Discover it® Miles card does allow you to use miles to cover the cost of tickets from Qatar, Emirates, or any other airline, but the card is not affiliated with either airline.
Here's how the card works and how you can use miles earned with the Discover it® Miles card to cover travel expenses. First of all, the card will allow you to earn 1.5x miles on all purchases without limits. So the more you spend, the more you earn. Once you have enough miles, you can start using them (Discover allows redemptions starting at 1 mile) to cover the full cost of an airline ticket or just a part.
To redeem Discover miles, buy a ticket from either Qatar or Emirates (or any other airline or travel agent) and pay for it with your Discover it® Miles card. Now you have 180 days to apply miles to the purchase. Once you apply your miles to the purchase, you will get a statement credit for the amount you spent.
In addition to travel redemptions, you can also redeem Discover miles as cash deposited to your bank account, use miles at Amazon.com or PayPal, or redeem as statement credits for purchases at restaurants and gas stations.
Either way you redeem, 1 mile is always worth 1 penny. So, to find out how many Discover miles you will need to cover the full cost of an airline ticket, simply add two zeros to the price and you will get the number of miles. Thus, if a ticket costs $394, you will need 39,400 miles in your Discover miles balance to cover the full cost of the ticket.