I did the same 6 month ago. please note the following :

New born baby must enter the country before 90 days. So they will issue the visa on arrival at the airport itself. Ask them or you to keep the vaccination card/details. Birth certificate needs to be attested by the Ministry of External Affairs in INDIA but NO need to verify the ministry of foreign affairs in QATAR.
After they came in Qatar you just go to any MoI Service center with Filled application form, birth certificate, original passport, your and Wife's passport and RP/ID copy and baby's photo with blue background. NO need for medical test. They will issue, print and stamp the RP on baby's passport same day. I finished these all process with in 30 mints...