Hi,
I'm not sure exactly where the Maori ancestry fits into your search is it Dorothy Ethel Phipps father or further back?
I also have a grandmother who had a child at the Carlton Women's Hospital and I have looked at their new web page which is the Royal Women's Hospital Victoria and they have an Archives centre with patient records up to 1889 online. They will provide information for births over 100 years old if they have it and you provide information that you are related. No promises that they will find anything.
http://www.thewomens.org.au/ArchivesIt's a lucky find for me too as I hadn't noticed before that they will provide information of deceased patients within the 100year time frame.
There is a mention on another page of costs involved so have a good look there are lots of internal links within the pages.
On the Maori issue I can only suggest listing on the new zealand forum and trying paperspast.natlib.govt.nz and nzhistory.net.nz The nz group have been particularly helpful and friendly with an issue I had.
Cheers
mabeljessie