It can be quite confusing. Have a go at the on line estimator, it will give you a bit of an indication of whether you are better off financialy to go with Paid Parental Leave or the Baby Bonus. Like BG said though consider you Child Care etc if that is applicable.

At present it is being paid by Centrelink, as of 1st July I believe they are phasing it in so that it will be paid via employers.

From looking at your Due Date I'd be calling straight away, you would rather get it sorted before bubs is born if possible.