You have not mentioned the name or sector of the company you have been offered a job. Anyways, for a government or semi-government company it takes a week to obtain a visa approval and for private companies approximately 2 to 3 weeks. Now as your visa request was submitted by the local sponsor on February 16th this confirms that the sponsoring company is pretty sure of hiring you, however, the visa applications are subject to ministry approvals. I suggest to contact the company and ask for your visa application number and you can check the status of you visa online by visiting www.moi.gov.qa click on VISA APPROVAL TRACKING you will get the details.