She won't be granted a family visa automatically, by default. She will have to meet the authorities, it might take time, and so on... It definitely won't be done in a first couple of months. If she is lucky, she will get it in 3-4 months. No one can promise "day one", simply because again as I sais, she has to get her own RP first. There are different ways to finally get to the point of RP. She might be able to keep her baby with her in Qatar from the beginning (although very tricky and uncertain) - there are visa on arrival for US citizens, family visit visa, etc., but if we are talking about Residence Permit, she has to keep in mind 3-6 months, not any less.
She won't be granted a family visa automatically, by default. She will have to meet the authorities, it might take time, and so on... It definitely won't be done in a first couple of months. If she is lucky, she will get it in 3-4 months. No one can promise "day one", simply because again as I sais, she has to get her own RP first. There are different ways to finally get to the point of RP. She might be able to keep her baby with her in Qatar from the beginning (although very tricky and uncertain) - there are visa on arrival for US citizens, family visit visa, etc., but if we are talking about Residence Permit, she has to keep in mind 3-6 months, not any less.