Cassie Sainsbury, 22, was stopped at an airport in Bogota on 12 April. She could face up to 25 years in jail, according to her sister, Khala.
The drugs were hidden inside 15 pairs of headphones that Ms Sainsbury bought during a holiday, the family said.
Ms Sainsbury's family claims she is innocent of drug trafficking charges.
Australia's Department of Foreign Affairs and Trade confirmed it was providing consular assistance, but did not give further details.
The personal trainer, from Adelaide, had just finished a working holiday when she was arrested at El Dorado International Airport, her family said.
Ms Sainsbury's mother, Lisa Evans, claimed her daughter was the "naive" victim of a Colombian man she had befriended during her trip.
"The day of her departure, he came up to her hotel, gave her a package that was wrapped in black plastic and she took it and put it in her luggage," she told Australian radio station KIIS FM.
"And this is where the naive bit comes in, she didn't even rip it open to make sure there were headphones in there."
They said she was being held at El Buen Pastor, Colombia's largest women's prison.
The family has started an online campaign to help cover legal fees, raising A$2,600 (Â£1,500; $2,000) in four days.
Penalties for possession, use, or trafficking of illegal drugs in Colombia are severe and offenders can expect long prison sentences under harsh conditions.
According to Ms Evans, Ms Sainsbury's lawyer has recommended a guilty plea to avoid a maximum sentence up to 25 years in jail.
If Ms Sainsbury pleads guilty, she would face a six-year sentence, which could be reduced further if she gives information about the man who supplied the headphones, Ms Evans said.
Colombia is one of the world's largest producers of coca leaves and cocaine.
Highly pure cocaine costs more than A$350 per gram in Australia, making it proportionally the most lucrative market in the world, according to the Global Drug Survey 2015,
According to a government website, Colombia's official working holiday visa may only be obtained by citizens of Chile, France, Mexico and Peru.

As well as the African Player of the Year and Africa-based African Player of the Year  shortlists which were announced last month, a range of other awards will also be handed out.
Continental successes feature heavily in the categories including nods to Nigeria's women's Nations Cup winners and Uganda's Gabon 2017 qualifiers.
Arsenal striker Asisat Oshaola, who finished as the top scorer with Nigeria at the women's Africa Cup of Nations in Cameroon, is amongst the names on the Women's Player of the Year shortlist.
The Super Falcons coach, Florence Omagbemi, is rewarded for Nigeria's triumph with a nomination for Coach of the Year.
She will face competition from, amongst others, Uganda coach Milutin 'Micho' Sredojevic, who guided the Cranes to their first Africa Cup of Nations finals in 39 years.
Also on that list is Pitso Mosimane who coached South Africa's Mamelodi Sundowns to the African Champions League title.  Sundowns are also on the Club of the Year shortlist.
Other names in the frame for an award are Manchester City's Nigeria striker Kelechi Iheanacho who is up for the Most Promising Talent prize, and fellow Super Eagle Alex Iwobi who features in the Youth Player of the Year category.
The winners will be announced at an awards ceremony in Abuja, Nigeria on Thursday, 5 January 2017.
Women's Player of the Year:
Most promising Talent:
Youth Player of the Year:
Coach of the Year:
Referee of the Year:
Club of the Year:
National Team of the Year:
Women's National Team of the Year:
An Australian woman has been arrested in Colombia after being found with 5.8kg (12lb 13oz) of cocaine in her luggage, her family says.
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The Confederation of African Football (Caf) named the shortlists for eight more categories ahead of its annual awards gala to be held in Abuja on 5 January 2017.