You can apply for an Austrian Identity Card (Personalausweis) at the Austrian Consulate in Melbourne. 

When travelling within the EU or within the Schengen area, a valid identity card can be used instead of a passport. 

The identity card serves as proof of Austrian citizenship and identity. Within Austria, the identity card is valid as an official photo ID.

The same documents are required for applying for an identity card as for applying for a passport.