No one has heard from her since.
Ms Davie was described on the New Zealand police missing persons register as being 163cm tall and of slim build. The register said all her belongings were left in her bedroom in Bridge End, Sydney, apart from a few clothes, which she was possibly wearing when she disappeared.
An inquest, which began in Sydney on Monday, heard police had been given a series of leads to follow up, but none had led anywhere, the Sydney Morning Herald reported.
One of these leads included a statement by a woman who said she had sat next to Ms Davie on a plane to New Zealand.
The woman said Ms Davie had told her she was sick of her boyfriend and was moving back to New Zealand for good, although when police checked the woman's details they proved to be false, leading them to believe the information was also fake, it was reported.
The inquiry also heard that at a party more than a year before Ms Davie's disappearance, a man had said she was "too trusting" and would be "easy to murder".
In April last year, 30 years after Ms Davie disappeared, Australian police offered an A$100,000 ($132,000) reward for information on the case.
After hearing of the reward, her Edgecumbe-based brother Nigel Davie said her disappearance and the past 30 years had been "devastating".
"We always think of her," he told the paper. Knowing what had happened would bring relief to him and his brothers, Mr Davie said.
- Additional reporting APNZ