We flew international when DS was 3 mths, however thought it would be a lot earlier, (that was 20mths ago) so unless something has changed all airlines had 7-10 day policy, nothing about immunization,
although our dr recommend to have them done, but that would depend on your dr, and whether your wanting to get bub immunised.
Otherwise GP, OB, maternal health nurse, all said that its perfectly safe for fresh bubs to fly
I bring it up next time you see your dr to put your mind at ease!
Hardest thing was getting the passport photo done!! Took two visits second time round got it after 40mins and they had to photoshop my hand out of shot