Hi, the process is fairly simple but not knowing all the answers might make it look complicated, so I have listed the process below and tried to answer your questions as part of it -

1. After application of the visa, the approval/rejection might come as soon as 1 working day or may take it's own time (on average 1 week). If rejected (yes, even after accepting your application it might be rejected for various reasons), you can speak to the immigration head and explain to him that your wife is pregnant (carry docs from Hamad as a precaution). You can check the status of the visa under 'Visa Approval Tracking' and once approved you can print the visa under 'Visa Enquiry & Printing' under the following link -
http://www.moi.gov.qa/site/english/

The above link is for English and you can also print the visa in Arabic by going to the Arabic site.

The visa is valid for one month and can be extended upto 6 months (including the initial month) once your mother-in-law is in Qatar.

2. Take a copy of the visa and go to Qatar Airways office and book a ticket with a return date within 1 month (as the initial visa is valid for 1 month). Do not forgot to ask the ticket agent to add the message 'OK to Board' on the ticket PNR as this would tell the Qatar Airways staff in your home country that the orginal visa will be stamped on arrival.

3. Send the ticket, visa, your passport copy, your wife's passport copy and marriage certificate to your mother-in-law. These documents should be enough, unless your home country has any other requirements such as travel insurance.

4. Once your mother-in-law lands in Qatar, the immigration staff will stamp one month visa on her passport. Within this one month you will have to get her medical done to extend the visa. The medical can be done at Medical Commission or at Ahli Hospital, Doha Clinic or Emadi Hospital. At the medical commission no prior appointment is required, your mother-in-law needs to present her passport and a credit/debit card of yours to make the payment. After she clears the medical (which you can check online), you can go to any immigration office and extend the visa upto a maximum of further 5 months - you can do this all in one go or every month. Once you have extended the visa, then you can extend the ticket.

All the best for the new arrival in your family.