This is up to your host. Some hosts prefer to do your laundry for you, others will put them in the washing machine for you but you will need to hang them on the line to dry. Other homestays will ask you to do your own laundry. You should speak to your host when you arrive to find out how you can do your laundry.
Please understand that, due to limited fresh water supplies in Australia, most hosts will ask you to wait until you have a full load of washing, not do 1 or 2 pieces at a time. Also, most hosts will not allow you to hang your washing in the bathroom or your bedroom, plus it is more hygienic to dry your washing and the fresh and sunny conditions. You should follow your host’s rules about where to hang your washing.