Thanks for looking that up. The first Daisy you sent, would actually have been the Aunt of the Daisy I am looking for. So if my Daisy was born here, then she might not have been registered, as the parents were on the run from solicitors.
All I have is 1903 born Australia, and the family were in USA by 1906. She is not registered in NSW or VIC. Have to check other states!!