Just a few thoughts:

1- Try contacting Visa or Mastercard directly (there should be a Middle East office). I guess you can file a complaint with them directly.

2- The air ticket bought should be very easy to trace and fraudster should be easily identifiable, issuing company (Visa or MC) should know what to do.

3- IMO, there is no point in not settling your genuine charges made on the card. I believe you settle those to show the bank good faith.

4- It is my understanding that there is a division in Qatar police department for electronic crimes, I suggest you inquire from this department what can be done.

Good luck and hope ppl here will be able to shed light on what to do