infants can travel entering Qatar on arrival visa if he/she has the following:

below 3 months old

has own passport

prepare birth certificate (better to be ready attest it because when you transfr them for family sponsored it will still be needed to be stamped by your foreign affairs office in your embassy before going to immigration)

keep his/her vaccination card for other purposes (you will need it later here in Qatar)

mother should be a resident under husband sponsorship.

and i think , from the date of arrival you are given 7 days to process the baby's iqama./residency.

good luck...