Hi hoola-hoop, I'm Marian, I work at the Department of Human Services in a team that responds to enquiries about Centrelink on social media sites like this one.
There are a few factors effecting a person's eligibility for a Centrelink payment when expecting a baby. If a person leaves their job to have a baby they may be able to claim the Newstart payment until the baby is born. There might be a waiting period, depending on how the employment ceases (i.e. if they leave voluntarily or if a contract is ended).
Newstart is a jobseeker payment and has 'activity' requirements. Expectant mothers can obtain an exemption from these requirements from six weeks prior to the expected date of confinement until six weeks after the birth of the child. If there are health problems outside of this period, an exemption may be granted under 'incapacity' (with a valid medical certificate).
There's more info about Newstart on the Human Services website here: http://www.humanservices.gov.au/customer/services/Centrelink/newstart-allowance The families page on the website has a lot of information about other payments and services such as Family Tax Benefit, Parenting Payment, Paid Parental Leave and the Baby Bonus. Check it out here: http://www.humanservices.gov.au/customer/subjects/families
Finally, another handy page is the online estimator here; http://bit.ly/gxTNCD You can enter information about your circumstances and it will give you an idea of your entitlements.
Hope that helps.