Thanks for your question Harald! Section 51(v) of the Australian Constitution gives the federal Parliament the power to make laws about ‘postal, telegraphic, telephonic, and other like services’. It does not say how these services will be provided, only that the Parliament can make laws about these areas.
Many other communication services, including radio, television and the internet are not listed in the Constitution (as they weren’t invented when the Constitution was written). In the Radio Licence Case of 1935 the High Court of Australia found that the Constitution gives the Parliament the power to make laws about all services which send communications over a distance by electronic means. Section 51(v) has since been expanded to allow the Parliament to make laws about new communication services.
The details of how these services are provided to Australians are contained in the various communications acts passed by the Parliament. The ComLaw website lists all laws passed by the Parliament.