If you were born in Australia on or after 20 August 1986 and one of your parents was an Australian permanent resident, you can provide evidence of your own Australian citizenship with a citizenship certificate issued by the Department of Immigration and Border Protection (DIBP). You will need to apply for this using Form 119 Application for evidence of Australian citizenship (pdf). You should take into account DIBP and passport processing times before booking any travel.
Alternatively, until 31 March 2016, we may accept your parent's foreign passport with an original visa label showing their status as a permanent resident at the time of your birth. You must have been born no more than five years after the visa was granted. If the visa was granted offshore, your parent must have arrived in Australia before you were born.
Further information can be found at the DIBP website.