http://www.australia.gov.au/information-and-services/immigration-and-visas/migration-to-australia
I can’t answer you, I know it’s not that easy. She could apply as a skilled immigrant...lol!
http://www.agriculture.gov.au/import/goods/live-animals
Not all live animals and reproductive materials are allowed to be imported into Australia; the pest or disease risks associated with their importation may be considered too great.
The links below provide the import conditions and quarantine requirements for pet animals that currently can be imported into Australia.
Birds Selected species from New Zealand only
Cats import via approved countries only
Dogs import via approved countries only
Horses approved countries only
Rabbits New Zealand only
Currently no other pet animals can be imported into Australia.