I think the answer is no unless you are a Australian Citizen. This is taken from their website To be considered for a job in Customs and Border Protection you must be an Australian citizen. If you are not an Australian citizen, but are eligible for citizenship, your application may be considered. You are encouraged to begin your application for citizenship if you are considering a position in Customs and Border Protection.
http://www.customs.gov.au/site/page4250.asp