A teenage mother who mistreated and murdered her 4-month-old baby after the "fantasy" of motherhood didn't meet her expectations shouldn't receive a life sentence, her lawyer has said.

Perth woman Cassandra Rose Doohan was 18 when she violently shook her baby Anastasia, causing the infant to die on May 2017.

Anastasia's father found her limp and "floppy" body in her cot after he came out of the shower and the baby died at Princess Margaret Hospital in Perth two days later.

The 4-month-old had suffered traumatic brain and spinal injuries as well as fractures and bruising.

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Doohan originally pleaded not guilty to murder but later admitted committing the crime.

Cassandra Doohan, 18, admitted to murdering her four-month-old daughter Anastasia. Photo / Supplied
Cassandra Doohan, 18, admitted to murdering her four-month-old daughter Anastasia. Photo / Supplied

Defence counsel Seamus Rafferty says Doohan's case was "exceptional" and she should instead be handed a fixed prison sentence rather than life for murder.

Rafferty said Doohan had a difficult childhood absent of love and devotion and had a violent and sadistic father.

He described Doohan as socially inept, who wanted a baby because she was fixated on the fantasy of creating a "perfect little world" for herself where she would be the perfect mother.

However, the reality was far different with Doohan not coping with the responsibilities of being a mother.

"When she had Anastasia, it simply became all too real," Rafferty said. "Her concept of motherhood was completely skewed."

The prosecutor said Anastasia had been seen with several bruises weeks before her death.

Child protection services had become involved.

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Justice Anthony Derrick said he needed more time to consider the submissions.

He will sentence Doohan on Tuesday.