You seem to have missed Mr.K's notation that it is unlikely that the Aussies will entertain a petition to change the name of a non-resident. You have to present them with damned good reason to do so, and "I don't want my daughter to have her father's name" is insufficient both here AND there.
You also seem to keep getting the order of things backwards. You have to be granted the change of name petition here first, before you can even consider petitioning in Oz to change the child's birth certificate - and even if it's granted here, there's no way for us to tell if Australian authorities will grant the name change there, even if your ex-husband consents. (For that matter, your ex-husband consenting is no guarantee the petition will be granted here, either. It's just not that simple.)
From where I sit, you're tilting at a particularly stubborn windmill, Madame Quixote.

