In australia its really hard to buy bitcoin being anonymous and with recent rule you can get caught if you are dealing more than $10,000 in cash within one year. Therefore you cant buy more than $10000 worth of bitcoin in ayear with cash. Also finding sellers who are willing to deal in cash or bank deposit is very rare in p2p platforms without identity verification.

From what i have learnt its impossible to buy bitcoin anonymously in australia but there is small loop hole which allow you to cash out bitcoin anonymously.