Dear ….
You can get a visa for her within 24 hrs … that’s Visit Visa for direct related persons like your wife your parents.
All you need to go for Immigration department at Airport (if you are moving from TOYOTA signal to VIP roundabout enter first right) and get an application … fill it and attach your passport copy (Name page + Validity) and resident permit page , your wife passport (Name and Validity) and if she has a GCC permit that’s will help much .
Submit with 70 QR cost … That’s all
And if she went out Qatar … next day or same day even you can apply for Permanent family residence visa .
Check also :
www.moi.gov.qa