Hello Musicman,
Normally for a Visa it doesn't take more then a week's time (actually the ministry take 1 day but other things included it may take max 1 week) You can access the MOI website with the link given below and keep checking your Visa application status. if at all HMC has already applied fora visa then you should see the status. You just need your passport number then select the country you belong to and it should give you the status.
https://portal.moi.gov.qa/wps/portal/MO … ndprinting
regards,
Kashif