These three jurisdictions can be covered by filing direct applications with each office: the USPTO (US), the EUIPO (EU), and IP Australia.
All three can be filed simultaneously. Non-US applicants filing with the USPTO must appoint a licensed US attorney. Non-EU/EEA applicants filing with the EUIPO must appoint an EU/EEA-based representative. IP Australia does not require mandatory representation for foreign applicants, but using a local trademark attorney is advisable.
The Madrid System can also be used to designate all three in a single application, provided you have a qualifying home application or registration to base it on. For these three jurisdictions specifically, direct applications are often preferred because each has distinct examination standards and the Madrid route adds a dependency on the home application for five years.