The mother-of-three went missing after dropping her daughter off in St Kilda on Thursday last week and flew from Christchurch to Brisbane the next day.
She was last seen at a Brisbane backpacker's hostel in Upper Roma St on Saturday, Brisbane police said yesterday.
Her handbag, containing her passport and driver's licence, was found under a bridge in Brisbane on Monday.
Her Melbourne-domiciled father, Peter Tocher, speaking to the Otago Daily Times from under the bridge where the handbag was found, said he and his wife, Jennine, arrived in Brisbane about 9.30am yesterday.
Being actively involved in the search was less stressful than waiting in Melbourne, he said.
''I don't know whether we are doing any good whatsoever but you've got two extra sets of eyes walking around the streets ... We love our daughter and we would do anything to make sure she is safe and we are doing whatever we can.''
Homeless people slept under the bridge where the handbag was found.
It was unknown whether their daughter had slept under the bridge.
The handbag appeared to have been ''abandoned'' rather than stolen and dumped as it was ''untouched''.
Yesterday, the couple created missing-person banners for display and searched for their daughter at various backpackers and public buildings such as libraries and museums.
''She is likely to be sitting God knows where - anywhere,'' Mr Tocher said.
She would be ''sweltering'' if she was still wearing a hoodie and tracksuit pants, he said.
Police were still reviewing the CCTV footage recorded across the city.
After arriving in Brisbane, the couple spent two hours talking to police at a central city station.
The police investigation in Brisbane had been ''fantastic''.
Police said a photo of their daughter would be posted on the police Facebook page.
The posts usually had an ''incredible response'' and provided ''quick leads'', he said.
''We hope the Facebook page is going to trigger somebody's memory.''
The post had been delayed because the missing-person file was emailed from Dunedin at 3pm on Monday.
The email did not automatically generate a missing-person file in Australia, he said.
The file creation in Brisbane yesterday was triggered by their visit, he said.
The couple had not booked return flights to Melbourne but believed the longer she remained missing, the greater the likelihood she was alive, he said.
The father of their daughter's youngest child was ''distraught'' but her three children were ''fine''.
''They are with their respective fathers and being looked after.''
