A Perth woman has pleaded guilty to murdering her baby daughter at the family's home in Capel, in WA's South West, but may escape a life prison term in what her lawyer described as an "exceptional" case.

Key points: Anastasia Hand suffered a catastrophic "non-accidental" brain injury in 2017

Anastasia Hand suffered a catastrophic "non-accidental" brain injury in 2017 Her mother, Cassandra Doohan, was due to stand trial but pleaded guilty to murder

Her mother, Cassandra Doohan, was due to stand trial but pleaded guilty to murder Doohan's lawyer called for a non-life sentence, which would make history in WA

Cassandra Rose Doohan, 20, had been due to stand trial next month over the death of four-month-old Anastasia Hand in May 2017.

But during a brief appearance in the Supreme Court on Thursday, she admitted the murder charge.

No further details were given, but a bail application when she was first charged was told Doohan had been left alone with the baby for about 15 minutes and when her partner returned from having a shower the baby was unresponsive.

She died two days later in Princess Margaret Hospital.

Anastasia died in Princess Margaret Hospital two days after the incident. ( Supplied: GoFundMe )

The court was told the baby had suffered a catastrophic brain injury that was described as non-accidental.

The bail application at the time was refused and Doohan has been in custody since her arrest not long after the baby's death.

Push to avoid life sentence

On Thursday her lawyer, Seamus Rafferty, told the court the case was "of such an exceptional nature" he would be arguing that his client receive a fixed jail term, rather than a life sentence, which is usually imposed for the crime of murder.

If Doohan is given a fixed term, she would become one of only a handful of people in Western Australia convicted of murder not to receive a life sentence.

Doohan has been in custody since she was arrested two years ago. ( Facebook: Cassandra Hand )

That follows changes to the law in 2008 under which judges can impose a non-life sentence where it is considered the offender does not pose a threat to the safety of the community, such as in cases of mercy killings or infanticide.

The sentencing judge can instead impose a finite sentence of up to 20 years.

Psychological and psychiatric reports will be prepared on Doohan in preparation for her sentencing hearing in September.

She was again remanded in custody after her court appearance on Thursday.