This is one of the more annoying airline rules and it's mostly about fraud prevention and not any specific legal requirements. Hence, you may be able to talk your way out of it but you probably need to improvise and sweet talk a bit. Here are some ideas:
- Call Qatar RIGHT NOW and ask them what to do
- Make a photo of your credit card (both sides) and sent the pictures to your friend
- Make sure both you and your friend both have online accounts and try to associate with the online account using the booking reference. Turns out, Lufthansa waives the "present credit card" rule, if you have an online account with them
- Make sure that your friend has all documents regarding the booking: receipt, confirmation, etc.
- Create a "letter of booking intent", where you inform the airline that you have indeed booked this ticket for your friend with your credit card, that he doesn't have physical access to this credit card and that you are willing to confirm this in whatever way the airline sees fit. Add you contact info.
- Make sure you and your friend can communicate during check in, i.e. cell phones charged and on proper access plans, be available during that time, etc.
The key here is that you or your friend need to convince the check in agent that the booking is real and not fraudulent. The agent (or supervisor) has the ability to waive the requirement, you just need to convince them to do so.