A South Australian woman who was cleared of being a member of the Islamic State terrorism group by an Adelaide court, after serving two-and-a-half years behind bars, is facing the prospect of having her acquittal overturned in the High Court.

Key points: Zainab Abdirahman-Khalif was found guilty of having Islamic State membership

Zainab Abdirahman-Khalif was found guilty of having Islamic State membership Her guilty verdict was overturned and she was released in October

Her guilty verdict was overturned and she was released in October However, an appeal against her acquittal was lodged on Friday

The Commonwealth Director of Public Prosecutions (CDPP) confirmed it lodged an appeal on Friday against Zainab Abdirahman-Khalif's acquittal.

The ABC understands the CDPP is appealing on the grounds South Australia's Court of Criminal Appeal "erred" in finding the prosecution had to prove how terrorist organisations admitted their members.

In overturning the conviction, Chief Justice Chris Kourakis said the CDPP did not produce evidence about IS's organisational structure or membership.

"No evidence was adduced on how members were recruited or selected, or of any process by which they were induced and finally accepted into the organisation," he found.

It comes as the Federal Court, sitting in Adelaide today, was forced to delay an application by the Australian Federal Police (AFP) for Ms Abdirahman-Khalif to be placed on a 12-month control order.

An interim order was put in place last month that limited the 25-year-old's social media use, movements, employment and prevented her from contacting anyone in Turkey, Syria or Iraq.

A three-day hearing has now been listed for April.

Federal Court Judge Natalie Charlesworth heard counsel for Ms Abdirahman-Khalif would call a de-radicalisation expert and psychologist to give evidence about what risk she posed to the community.

She questioned the three-month delay in hearing the application, saying it would be unfair for Ms Abdirahman-Khalif.

"It's a long time for someone to be subject to a control order, which may be revoked," Judge Charlesworth said.

Zainab Abdirahman-Khalif was acquitted in October of being an IS member. ( Nine News )

But James Caldicott, for Ms Abdirahman-Khalif, said he needed the three months to mount a defence against the application.

Ms Abdirahman-Khalif was acquitted of being an IS member in October after spending two-and-a-half years behind bars for the offence.

Last month, the Federal Court was told anti-terrorism police had deemed Ms Abdirahman-Khalif not to pose a risk to the public and a terror attack was "not expected" because she lacked the skills and knowledge to carry one out.

Commonwealth prosecutor Andrew Berger told the court that laws were designed to "prevent 'a' terrorist act, not 'her' terrorist act" and to "protect the public from the threat of a terrorist act".

"It's not punitive — it's not to punish [Ms Abdirahman-Khalif] for what she has done or what she thinks. It's to protect the public," he said.

Detained at airport with one-way ticket to Turkey

But Marie Shaw QC, for Ms Abdirahman-Khalif, previously said the court must be satisfied, on the balance of probabilities, that it was likely a terrorist act would occur if a control order was not made.

During a three-week trial in 2018, the Supreme Court was told that Ms Abdirahman-Khalif was detained at Adelaide Airport in July 2016 after buying a one-way ticket to Turkey, and that she planned to travel with $180.

She was released from custody the following day and about 10 months later was charged with knowingly being a member of a terrorist organisation.

The court heard 378 audio files associated with IS were found on her phone, along with 125 videos — 62 of which contained extremist material including bombings, executions and dead bodies on the ground.

Ms Abdirahman-Khalif was also in contact with three women who carried out an attack in Mombasa, Kenya, for which IS claimed responsibility.

Justice David Peek sentenced the woman to three years in jail with a non-parole period of two years and three months, backdated to May 2017 when she was taken into custody.

Her former sentence was set to expire in May 2020.