The Qatargas accommodation is in Al Khor, but it's so full that lots of staff working in Ras Laffan live in Doha and commute via private vehicle or via Company provided buses. Your best option is either to live in Doha or outskirts and commute to Ras Laffan. I'm sure you can find someone to share transport with if you chose to stay in Doha.

As for Hospitals, Al Ahli is the hospital Qatargas sends it staff to so that would probably be your best option. However, I have a friend that had emergency C-Section at 31 weeks due to pre-eclamsia and she delivered at Hamad. She said they were really great and she had a room to herself. They are also much cheaper than Al Ahli.