My boys have British passports. Their dad is Scottish. So may be a slightly different process so I looked it up and looks like you need to register your baby's birth in the foreign birth register, once registered they are an irish citizen and you can apply for their passport online and submit the necessary documentation like their birth certificate and your birth certificates (to name a few) pay the application fee and submit the application then the passport will be delivered. I don't think they deliver it to Aus but will need to deliver to a more local address then they will need to forward the passport to you.
hope that helps!
My boys have British passports. Their dad is Scottish. So may be a slightly different process so I looked it up and looks like you need to register your baby's birth in the foreign birth register, once registered they are an irish citizen and you can apply for their passport online and submit the necessary documentation like their birth certificate and your birth certificates (to name a few) pay the application fee and submit the application then the passport will be delivered. I don't think they deliver it to Aus but will need to deliver to a more local address then they will need to forward the passport to you. hope that helps!