Will it be quicker if I post my passport application form to Ireland?

No. You must not do this.

Applications from Irish citizens resident in Australia must be made at the Embassy of Ireland in Canberra or the Consulate General of Ireland in Sydney (NSW) or the Honorary Consulate in Perth (WA) only.

Applications made directly to Ireland will be returned to the Embassy for processing causing additional delays.

If you submit an application in Ireland a witness must verify that you live in Ireland. Submitting an application with a false declaration is a serious offence. If the Passport Office see that you live in Australia, they will reject the application.