Well according to my knowledge with the immigration rules and regulations I would suggest that you have to apply for your wife a re-entry visa through immigration not in the airport. They will provide you a re-entry visa for a miximum period of 45 days. Then you can send a copy of re-entry visa to her so that in the airport she will not have any problems.

But as rules changes every time its better to bring her to qatar and if she wants she can trave back after a week stay in qatar where your old visa gets into live without expirying (as she overstayed outside of Qatar for a period of six months).

Thank you