The Constitution provides the subject matters of which the Commonwealth has its law making powers, within those powers are limited health powers. Section 51(xxiiiA) is known as the funding power of the Commonwealth, which is a power to fund medical and dental services, pharmaceutical benefits and alike.
The States hold the power to regulate health, that being the power to regulate health services and those that provide such services. The Commonwealth and the States have absolutely no power to regulate you the patient. The doctor-patient relationship is a private contract in law (Breen v Williams 1996 HCA), it is private, voluntary and by consent. It is clearly not within the power of the Commonwealth to recommend any medical procedures or services such as vaccination.
See response to a FOI request: