It will cost you around 1500 QR a month for a live-in maid. It will cost more for a nursery and nurseries usually only run until 2 or 3 in the afternoon. Check the bottom right side of this page in Qatar schools database to find out about nurseries.
As for the safety of leaving a baby--that depends on your comfort level. I think it would be terrifying to leave a tiny baby with either a maid or a nursery, but if you have no choice, you do what is the best for your family.