It is difficult to obtain exact information on the waiting period as it is case dependent. Some suggest that shorter stay visas can take up to 15 days whereas permanent, long-term visas can take up to 8 weeks.
The best way to find out how long the process will take is to apply and consult the relevant sources directly. For some information on how to do this take a look at another of our threads about Qatar visas.
Would you be able to tell me how long it took for your visa to be processed? .... My husband just accepted a job with Qatar Airways and I am in a similar boat, trying to figure out the timeline for the family visa to be approved.