What is the process for changing a Visitors' Visa into a Work Permit?

My family and I came to Qatar approximately 6 months ago on visitors visas. Recently, I was offered a position working in the education field. The company wants to bring me under their sponsorship. From what I understand, after my paperwork is completed and I am issued my work permit, I will have to apply for my family to be placed under my sponsorship. Does my family have to leave the country and return on a new visa or can this transfer be done without them having to leave the country?

Additionally, my embassy has suspended services to its citizens for administrative reasons. Does anyone know how long parents are given to obtain their newborn's passport for the purpose of getting his/ her visa? Also, will the airlines allow a newborn to fly (without a passport)?