If you recently got married in Australia or a baby was born, you should register the event in the Estonian Vital Statistics Register. It is free of charge and can be done via the Embassy of Estonia in Canberra.
First, you should apostill the original Australian marriage certificate/birth certificate.
Once the certificate is apostilled, send the original to the Embassy with passport copies of both spouses/both parents. On passport copies write „True copy“ + date + signature. Add an empty self-addressed express post envelope for returning the original certificate.
Embassy of Estonia is located at:
12 Darwin Avenue
Yarralumla ACT 2600
By registering your child in the Estonian Vital Statistics Register he/she automatically receives Estonian personal identification code.