hi
First your visit visa came out from imagration not from airport

ok
you need to fill up a form and submit to labor office attached with letter from your ompany with the salary and bank statment you have to mintion the visa no in the applacation form
and if your paper accepted they will issue a new vis risidancy visa for your wife

no need to go out Qatarto have that
u will go to immgration and ther they will stap the new visa issued to the passport of your wife
cost for that (500)qr
when it done you can start the iqama residanet paper for you wife (medica finger peint iqama )
hope that info was usful