The Department of health indicates that “Optimal protection against influenza occurs within the first three to four months following vaccination. Timing of vaccination should aim to achieve the highest level of protection during peak influenza season. This usually occurs from June to September in most parts of Australia. Vaccinating from April provides protection before the peak season.” https://www.health.gov.au/news/clinical-update-2020-seasonal-influenza-vaccines-early-advice-for-vaccination-providers
Canberra
In Canberra Capital Health Care Pty Ltd vaccinates from 14th April to 22nd May. The first half of May is normally recommended to provide optimal protection from Canberra's longer winter.