There is a reciprocal medical provision agreement between the UK and Australia, which guarantees free healthcare for unforeseen medical conditions provided by Australian Medicare. The provision does not extend to pre-existing conditions or for drug prescriptions except as a hospital in-patient. Therefore, you should still ensure that you have comprehensive travel insurance in case of an emergency.
Although Australia is Malaria free, there are incidents of other insect borne diseases in many areas of the country, and you should take appropriate measures to protect yourself while in the country.