Is the Queen of England also the Queen of Australia?

Australia decided not to become a republic. Because of this decision they also decided to take many British customs (the flag,i.e) they also let the beloved Queen of England have a title. It is to be understood though that the Queen of England has absolutely no power in the world.... she just waves and smiles.... that is her position in other Words... and the same is to her title in Australia... waving and smiling.... she has a title for Canada also.