To purchase a ticket at qatarairways.com where the card holder will not be one of the travellers, follow these steps:
Start the booking on qatarairways.com and when the system asks "is the payment card holder travelling on this booking," click Yes.
Under this scenario, the credit card holder would need to accompany the traveller(s) to the airport check-in counter (he/she would need to have the physical credit card and a valid ID or passport with him/her).
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The credit card card holder may present themselves at a Qatar Airways office (he/she must have the physical credit card and a valid photo ID or passport).
Visit the nearest Qatar Airway office to complete in a 3rd party payment form at least 3 days in advance of travel.