I would be careful with this one, ask immigration. You may need a letter to allow the baby to enter Qatar. Remember, Qatar attaches the children to the father, not the mother, and 10 chances to 1 they may not even allow your wife to leave India without a visa.

2 month old babies only cost 10% of the ticket cost, up to the age of 2 where you have to pay 75% of the cost.

Bald, 2 month old babies sleep most of the flight anyway. It is the older drunks on the plane who are the most disturbing to passengers.