No advice on the centrelink payments as we never qualified for any but exactly what Divvy said - you'd be amazed at how much you can save if you are conscious of what you are/are not spending.

Make a list of all the things you have for bub and what you are still needing. Maybe speak to family and point them in the right direction of things that you need so that you can get things you will use instead of kazillion soft toys like we ended up with.

Good luck!