The recent announcement of teachers, teacher aides, school staff and early childhood educators being eligible for the vaccine was a QLD Health decision and is only applicable to QLD health clinics.
At this stage the Commonwealth eligibility has not changed.
Teachers and other applicable staff who are not eligible under any other criteria can access their vaccine by registering via QLD Health.
https://www.vaccinebookings.health.qld.gov.au/registerforvaccination/