Earlier, one could get it in just a day if the applicant met all the requirements of the government but this could have changed due to FIFA. You can this by going over to any of the passport and immigration office in Doha. Avoid going the passport & immigration office at Gharaffa as usually it is very crowded. Also, the facilities at all offices are the same. As for changing a visit visa to a family visa, talk to the PRO of your office for guidance. You may also get some advice from people who do typing jobs around Doha usually known as "Hukumi".