Firstly the baby bonus is only $4,133. It will be indexed this month and will be slightly more, but I don't know if it is indexed at the start or the end of the month.

When bubs is born they will give you the necessary paperwork to fill in as they need to put a label on the back stating that the baby was born at xyz hospital, the midwife and Dr attending and date etc. They will also give you a form from Births, Death's and Marriages to register the birth and one for medicare as well. You then send the forms into all the necessary departments with the correct paper work. If this is your first time claiming from Centrelink, you will need to provide a fair amount of information but on the guide book for the form it will tell you what you need.