We are also taking our departed dog in a wooden container.
Yes you can bring ashes into Australia no problem check this site out to confirm http://www.daff.gov.au/aqis/faqs#1s,
Only just found this thread after having a good nose around. We recently lost our staffie :(and I was thinking the same thing as we have his ashes in a wooden box.
I asked a removal firm and this is the reply i got :-
You can definitely ship your pet ashes. This is not a problem, and we have
had previous customers do this.
You will need to have a certificate completed by your vet, to confirm the
remains, and the cause of death, but as far as I know, an import permit
isn't required by AQIS (Australian Quarantine and Inspection Service - equiv
I would recommend having a look at the AQIS site yourself, or even
contacting them to enquire further, but as for the actual shipping, this is
definitely allowed, and has been done before.
Hope this helps.
I am taking my Dalmations ashes too. His ashes are in a sealed plastic bag in a porcelain urn. If I couldn't have taken him I was going to bury his ashes by my Nan who passed away this year. She loved him to bits. But thank goodness he can come. Bit worried about a death certificate though as we no longer live in the same area and he died 9 years ago!!!
I'm also taking my border collie's ashes who passed away about 5 years ago with me (we're a daft bunch aren't we - wouldn't dream of leaving them behind though). I'll contact the agents again and see what they say about a pet that passed away so long ago - maybe you won't have to bother.