In answering this question there appears to be no law currently in place in Australia that prevents a person shooting in their backyard, although Archery Australia is not a legal expert and formal legal advice should be sought before you undertake such an activity.
Points to consider: is the property a rental property, units or housing complex or a privately owner/occupied dwelling? For rental properties, units and housing complexes check with the property owner or body corporate. This may vary from State to State and there may be specific laws regarding types of properties.
You should also check your personal household and public liability insurance policy; you may not be covered for such an activity.
You are NOT covered by the Archery Australia's insurance policy when shooting in your backyard. Archery Australia's insurance only covers current financial members when engaged in archery activities at approved venues detailed in the Certificate of Currency and accompanying documents.
Be aware, when engaged in archery activities on private
property, although there appears to be no specific laws covering this
activity, action could be taken by Police following a complaint
resulting in charges for Making a Public Nuisance, Discharging a Weapon
or Endangering Public Safety.
You should also be aware that, if an arrow enters another person's property, you could be changed with Trespass and if the arrow strikes or damages another person's property further charges could be follow.
The recommendation from Archery Australia is that you DO NOT shoot in your backyard. However, if you do, you must ensure you have the appropriate permissions from the property owner and that you have appropriate property and personal insurance cover. Also you should undertake an appropriate Risk Analysis of the planned activity.