Property Buying Restrictions:
Australian Citizen or Permanent Resident - No Restrictions
Temporary Resident, Retiree or Student - Can buy new property without restriction or an established property provided it is your residence and it is sold when your visa expires. Consent of the FIRB is normally required. (exceptions apply for some spouse / de facto partner.)
Foreign National or Foreign Corporation - Can buy new property. Can buy vacant land as long as building commences within 12 months of purchase. Can buy an established property only if an additional amount of no less than 50% of the original property cost is spent on improvements or additional construction. Can buy up to 50% of new projects or apartments, Consent of the FIRB is required.
FIRB = Foreign Investment Review Board -
http://www.firb.gov.au/
Interesting Q&A fact sheet: -
http://www.firb.gov.au/content/faq.asp