Skull flyer,
They have a choice and you have a choice. Tell them 777 or 787 or no deal (if asked). In any interview, explain your prefernce and why a heavy Boeing slot makes sense for them and you. May not work, but you have heavy Boeing experience and both of those fleets are growing. They may say no and then EK and the other big UAE carrier become better options. I still think Emirates is probably the better way to go from an overall package if you ever had the choice - but others may disagree. Apply to the big 3 if you want the ME and roll the dice. The Qatar HR group has been an utter disaster with poor communication and a disorganized process. From what I have been hearing, don't be surprised if things go silent for long periods and don't expect Western standards of communication.
Good luck