Could you study something with employment prospects given your field doesn't have many? My understanding is post grad would be 1-2 years and you could work for a little while and have access to Government paid parental leave as well as possibly parental leave from your employer? That would ease the financial burden somewhat.
For what it's worth I don't actually see anything wrong with you having another now if you'd like to and can financially survive on the pittance Centrelink provides! I, like a PP, would love to be able to do that but our circumstances don't afford us that choice.