Top tip: Do not resign from your current position until your visa has been issued.

Depending on your employer and/or how much 'wasta' (influence/connections) they have, it could be three weeks, or it could be three months or longer. Do not make the mistake others have of resigning from your job, because if your visa doesn't come through promptly, you may end up spending some time 'between jobs', unemployed and not earning.

Sometimes it depends on what nationality you are, for example if you're a citizen of a country that doesn't have particularly good relations with Qatar at the moment.

People with dual citizenship may also experience longer delays.

The answer to your question is basically the same as the answer to the question: how long is a piece of string?