Here's the US regulation. http://www.cdc.gov/quarantine/human-remains.html
There are no requirements for importation into the United States if human remains consist entirely of the following:
human remains that are cremated before entry into the United States
Cremated human remains, because they do not pose a
quarantine risk, do not require a death certificate. However,
it is recommended that when transporting the cremated
remains that the importer should carry a copy of the death
and cremation certificate and ensure that the remains are in
a container that can easily be scanned (e.g., cardboard,
wood or plastic).
Doesn't say anything about the ziploc bag.
Cremated remains may be carried by a passenger or they can be sent to Australia via Australia Post, air freight or sea freight.
If you are a passenger and are bringing in cremated remains, you do not need to declare the remains to Customs and Border Protection or DAFF Biosecurity, as they are not a prohibited or controlled importation. Nor do you need a permit or special permission from Customs and Border Protection or DAFF Biosecurity to bring the remains to Australia.
And Australia is pretty strict.