A starting point might be to get the birth certificate for Mary. This will give you her parents personal details and they might be easier to trace. Their newspaper death notices should provide details of their descendants and possibly their locations at the time. This would narrow your search area considerably.
Looking at the Tasmanian BDM website births are closed for 100 years BUT are available to a child of the person on production of a relevant document. Your pre-adoption birth certificate should fit this category.