Child protection authorities were alerted to the mistreatment of a baby girl 16 days before her mother violently and fatally shook the infant at the family's home south of Perth, the WA Supreme Court has been told.

Key points: Baby Anastasia Hand was seen with head and neck injuries six days before her death

Baby Anastasia Hand was seen with head and neck injuries six days before her death Cassanda Doohan initially denied doing anything before admitting to the murder

Cassanda Doohan initially denied doing anything before admitting to the murder Her lawyers have urged the judge to take the rare step of not issuing a life jail term

Four-and-a-half-month-old Anastasia Hand died in hospital from multiple injuries in May 2017, two days after her father found her unresponsive in her cot.

Her mother, Cassandra Rose Doohan, 20, has pleaded guilty to her murder, with the court hearing it was likely she had snapped when the child was crying.

A post-mortem examination found the cause of the baby's death was head and neck injuries.

But a range of other injuries, some of which were already healing, were also found, including numerous broken bones.

State prosecutor James Mactaggart said it was "highly likely" the injuries were suffered either days or weeks before the fatal assault, adding that it appeared Anastasia "had been subjected to other ill treatment" in her young life.

The court heard that in the weeks before the murder, Doohan's relatives had noticed injuries on the baby, including bruises, a scratch on the face and a friction burn to the neck.

Anonymous tip-off failed to prevent murder

At one stage Anastasia was taken to Bunbury Hospital, but Doohan claimed the injuries were a result of the baby rolling around in her cot and hitting her head on the rails.

The doctor decided the injuries were accidental, but an anonymous tip-off was made to child protection authorities who contacted Doohan and her partner and set up a safety plan.

Anastasia was found by her father floppy and not breathing properly in her cot. ( Supplied: GoFundMe )

Despite that, 10 days later and six days before the murder, relatives saw Anastasia with bruising around the neck and a blood clot over her eye.

Mr Mactaggart said when the baby was crying, Doohan was seen shaking her "violently" until she stopped, before putting her back in her pram.

The court heard on the day of the fatal assault, Anastasia's father changed the baby's nappy and gave her a bottle before going to have a shower.

When he returned he found the baby floppy and not breathing properly.

He immediately started CPR while Doohan drove to her mother's house, telling her, "Mum, mum, my baby's not breathing".

Doohan 'not equipped in any way to be a mother'

Doohan repeatedly denied to police that she had done anything to the child and had been due to stand trial earlier this year, but in May she officially admitted the murder charge.

Her lawyer Seamus Rafferty said his client was "simply not equipped in any way to be a mother."

Cassandra Doohan's lawyer has called for a fixed jail sentence rather than a life term. ( Facebook: Cassandra Hand )

He said until the age of four Doohan was exposed to violence by her father, whom Mr Rafferty described as "a drug-using sadist".

Mr Rafferty told the court the man used violence against Doohan's mother and herself, saying his client used to hide in a cupboard so he could not find her.

He said after that relationship ended, her mother started another, but Doohan did not assimilate into the "mixed home" and had numerous hospital admissions and psychiatric interventions between the ages of five and 14.

He said as a result Doohan had personality traits that were "disturbing", but she had decided to have a child because she wanted to feel the love of another.

"She had the fantasy in her mind if she had a baby and a partner … there would be this perfect world and everybody would be happy," Mr Rafferty said.

But he said Doohan did not understand the reality of having a child and she did not bond with Anastasia, "because the child was not complying with the fantasy in her mind".

Defence urges judge to avoid life jail term

Mr Rafferty said while he was not laying any blame, there were "a number of systemic failures" in the case, and while the authorities had become involved "whatever they did simply wasn't enough".

"There were clearly signs there that Anastasia was being mistreated," he said.

Mr Rafferty has urged Justice Anthony Derrick not to impose a life jail term on Doohan and instead to give her a fixed sentence, arguing the details of the case were "exceptional and extraordinary".

If that happens, Doohan would be only the second person in WA not to receive a life jail term for the offence of murder, following changes to the law in 2008.

Details of the previous case are suppressed.

The state is calling for a life jail term for Doohan, saying the baby was subjected to "a catalogue of mistreatments".

Doohan, who has been in custody since her arrest in June 2017, will be sentenced on Tuesday.