Is it just me, or is that tuba Limey is playing farting "69" out the bell?
Queen Liz is just a bit of decoration for us. Technically she chooses the Governor General from a shortlist, and this person has the power to dismiss the government and call an election; but a precedent has been established that you can give her a list of one name and let her choose from that.
Culturally, having a monarch does maintain our bond with the British culture that is the foundation of modern Australian culture; it provides a continuity during a time of cultural diversification. That and the cricket and rugby. And the language.