A young West Australian mother who violently shook her baby daughter to death has failed to convince a judge she should escape a life jail term for the murder.

Key points: Anastasia Hand died of head and neck injuries inflicted by her mother

Anastasia Hand died of head and neck injuries inflicted by her mother Cassandra Doohan lied about assaulting her baby before admitting to murder

Cassandra Doohan lied about assaulting her baby before admitting to murder Her lawyer said she was not equipped to be a mother due to her violent upbringing

Cassandra Rose Doohan, 20, had argued that the "exceptional" nature of the case meant she should receive a fixed term for the murder of her four-and-a-half-month-old daughter Anastasia, who died in hospital in May 2017.

Two days earlier the baby's father had found the child floppy and unresponsive in her cot, after leaving her alone with Doohan while he had a shower at the family's home in Capel, south of Perth.

On Tuesday Justice Anthony Derrick ruled the crime was so serious that only a life sentence was appropriate, and ordered that Doohan serve at least 13 years behind bars before she can be released.

The Supreme Court was told the baby died of head and neck injuries, but a post mortem examination revealed Anastasia had numerous other injuries including broken bones that were likely to have been inflicted in the days and weeks before the fatal assault.

Doohan, pleaded guilty to her murder, with the Supreme Court hearing she also admitted mistreating the baby in the weeks before.

A post-mortem found Anastasia had a range on injuries, including broken bones that were already healing. ( Supplied: GoFundMe )

The court was told Doohan's relatives had regularly seen injuries on the baby, including bruises on her face, a friction burn to her neck and a blood clot over her eye.

The baby was taken to hospital about two weeks before her death, but Doohan explained away the injuries as being a result of Anastasia scratching herself and rolling around her cot.

Someone anonymously tipped off child protection authorities and they visited Doohan and her partner before setting up a safety plan for the family.

But five days before the fatal assault Doohan's brother witnessed her holding Anastasia out in front of her and under the baby's arms, violently shaking her until she stopped crying.

Doohan's lawyer, Seamus Rafferty, said it was likely that same scenario played out on the day of the murder and his then 18-year-old client just "snapped".

Doohan repeatedly denied doing anything to the baby and had been due to stand trial earlier this year, but two weeks before the scheduled start of the case she changed her plea to guilty.

A motherhood fantasy destroyed

Mr Rafferty detailed Doohan's troubled upbringing, including being subjected to a "violent and sadistic" father until the age of four, followed by repeated hospital admissions and psychiatric interventions in subsequent years.

The court heard Ms Doohan suffered violent physical abuse herself as a very young child. ( Facebook: Cassandra Hand )

He said that led to his client developing "disturbing" personality traits which left her "simply not equipped in any way to be a mother".

Mr Rafferty said Doohan had decided to have a baby because she wanted to feel the love of another, but the reality of having a child was very different.

"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 bond with Anastasia, "because the child was not complying with the fantasy in her mind".

He said Doohan acknowledged her continued mistreatment of Anastasia but he submitted the murder was an impulsive act and Doohan would pose no risk to the community when she was released from prison.

Mr Rafferty argued because of the "extraordinary" and "exceptional" nature of the case, Doohan should not receive the life sentence that was usual for convicted murderers.

Doohan's actions 'dreadful': judge

Justice Derrick described Doohan's actions as "dreadful", saying she had taken the life of a completely defenceless baby.

He accepted that her culpability was reduced by her traumatic upbringing, her immaturity and the personality disorders she suffered, but said her actions were not the first time she had used excessive physical force against her child.

The court was told the baby's father had blamed himself and now suffered depression. ( ABC News: Briana Shepherd )

He also noted that instead of immediately seeking help after shaking her baby, Doohan had placed Anastasia back in her cot and not sought any help for her.

Justice Derrick referred to victim impact statements provided by Anastasia's paternal grandparents, where they said the effect on their son — Anastasia's father — had been extreme.

They said he now suffered depression and they doubted he would ever fully recover.

It was revealed that after the baby's death he felt he was responsible, believing Anastasia must have drowned on her milk because he did not burp her properly.

The court also heard that in interviews with police after the murder, Doohan named him as a possible suspect while refusing to accept she had done anything that caused Anastasia's death.

Doohan has been in custody since her arrest in June 2017 and with time already served she will become eligible for release in 2030, when she will be 31.