I actually rang Centrelink about this just today. It does get paid automatically into your bank account (provided they have your bank account details on file). They automatically check a child's records when they reach 19 months of age (varicella jab due at 18 months). In any case, they just wait for notification from the immunisation provider (GP, local council) and then process the payment.

I assume if they don't have your account details they send a cheque, I didn't ask though, because they have mine from when I got paid the baby bonus.

It gets paid before the child turns two (provided all jabs are up to date). As for the amount not sure of the exact amount, think it's about $200???