Aside from Hamad Hospital, you can also try Al Emadi Hospital, they have good facilities too. As for the visa, I think you have to apply for a family resident visa for your wife first because once your wife is on the husband's visa it will be easy to obtain a visa for your baby especially in this case that baby will be delivered here in Qatar. Seek your company's help because you would need NOC from your company and a form to be filled up with your employers/company's signature and stamp. Congratulations and all the best!
Aside from Hamad Hospital, you can also try Al Emadi Hospital, they have good facilities too. As for the visa, I think you have to apply for a family resident visa for your wife first because once your wife is on the husband's visa it will be easy to obtain a visa for your baby especially in this case that baby will be delivered here in Qatar. Seek your company's help because you would need NOC from your company and a form to be filled up with your employers/company's signature and stamp. Congratulations and all the best!