Children's books that I recommend that are set in, with characters from, or written by people from Australia:

Over in Australia: Amazing Animals Down Under by Marianne Berkes
Koala Lou, Possum Magic, and other books by Mem Fox – Fox lives in Adelaide, Australia
Diary of a Wombat by Jackie French
Edward the Emu and Edwina the Emu by Sheena Knowles - Knowles was born in Geelong, Australia 
One Very Tired Wombat by Renee Treml

For a thorough explanation of the history of children's books in Australia, the current children's book climate in Australia, as well as the past and present children's authors of Australia, you must check out: http://australia.gov.au/about-australia/australian-story/austn-childrens-books  It's a wealth of great information about children's books in Australia!