They had been in New Zealand for nearly 10 months, were settled here, had friends, family and were financially stable.
The mother was not in a relationship with the father, but had been living on and off with him throughout her daughter's life, including up until their departure date.
They had no family support in Australia, apart from the father, and as the mother was not an Australian citizen, her access to governmental support was much less than in New Zealand.
She was seeking employment in New Zealand but for the meantime was on a benefit here.
If she had to return to Australia she would not have any housing or employment options.
"We wouldn't have any other options."
The father's lawyer directed Herald inquiries to New Zealand's Central Authority, which is hosted by the Ministry of Justice.
The Herald has been unable to make contact with the father.
The pre-hearing is set for this Wednesday in the Christchurch Family Court, before a hearing takes place November 15.
In a statement, Ministry of Justice chief legal counsel Jeff Orr said the Central Authority could not comment on the case as it was before the courts.
Under the Hague Convention a person with child custody rights could seek the child's return if the removal of the child was claimed to be in breach of their custody rights "so that matters about the child's care and welfare can be decided in that country and in accordance with the domestic law", Orr said.
The Convention aimed to protect children from the harmful effects of their wrongful removal or retention.
"It does this by ensuring their prompt return to the country where they normally live unless one of the grounds for refusing return is established. A key principle of the Convention is that it is the court in the country where the child or children normally lives that is best placed to make decisions about care and living arrangements because they have access to all the relevant information."