The six-month-old girl drowned in the bath-tub of a North Strathfield home in November 2010 after her mother had worried obsessively for months that the infant had dwarfism or another genetic disorder.

The woman, who cannot be named for legal reasons, pleaded not guilty to murder on the grounds she was suffering from a mental illness at the time, but guilty to manslaughter.

The plea was accepted by the Crown last month.

During a sentence hearing in the NSW Supreme Court on Friday, the woman's barrister Peter Lange urged Justice Robert Beech-Jones not to impose a jail sentence, but to consider a bond or a suspended sentence.

"No court could ever inflict a punishment greater than the death of her daughter, by her," Mr Lange said.

The woman, 41, has already spent almost a year on remand, including time in the forensic hospital at Malabar, and a further eight months on quasi-remand as an inpatient at a forensic unit in western Sydney.

A number of forensic psychiatrists agree she had a pre-existing schizoaffective disorder but was high functioning and held a managerial role at a professional firm before her daughter's birth.

However, she experienced a "significant deterioration in her mental state" within 24 hours of giving birth to her daughter in April 2010 and rapidly spiralled into post-partum psychosis and depression.

Just after midday on November 18, 2010, the woman called triple zero, saying her baby was submerged in the bath, having fallen from her bath seat.

Despite the operator's attempts to get her to go back inside the bathroom to retrieve the baby from the water, she refused, saying: "I can't go in there."

Paramedics found the girl naked and face down in the bath-tub.

An autopsy revealed the baby had marks on the back of her head consistent with fingernail scratches.

Later that day, the woman was admitted to the psychiatric wing of Concord Hospital.

An agreed statement of facts tendered to the court show the mother had begun worrying obsessively that her daughter had genetic abnormalities soon after the birth.

The baby was tested for conditions including achondroplasia or rhizomelic shortening (dwarfism).

Though examinations cleared the baby of any condition, the mother remained highly anxious and doctors arranged X-rays and genetic testing to ease her concern.

She told staff at the Sydney Children's Hospital: "Every time I look at her, she looks like a dwarf ... it's affecting my bonding with her, and everyone in the family including my husband thinks I'm crazy."

By the end of October, the woman had been assured all the tests were "normal" and "no abnormality" was detected, but her levels of anxiety increased and she continued to believe the girl was abnormal.

During the months of testing, the mother spoke a lot to friends about the way her baby looked and what might be wrong with her. One friend said she brought the girl to a child's birthday party on a warm September day dressed in a hooded suit to hide her skin tags. At the girl's six-week check, she had asked the paediatrician when she could have plastic surgery to remove the tags.

A forensic examination of the woman's computer identified thousands of internet searches for dwarfism, various conditions and surgical rectification.

In February 2014, she was found unfit to be tried. In December 2014, at a special hearing, NSW Supreme Court Justice Geoffrey Bellew found, on the limited evidence available, that she had committed the offence of murder.

He ruled she could be detained at a facility chosen by the Mental Health Review Tribunal for a maximum of 20 years.

By December 2015, the woman's condition had improved and her psychiatric illness was said to be in remission and the tribunal found she was fit to be tried.

The Crown agreed that, at the time of her daughter's death, her "capacity to understand events, judge whether her actions were right or wrong and to control herself was substantially impaired by an abnormality of the mind arising from her underlying condition".

Mr Lange said she was a "loving and devoted mother" and the death "would not have occurred had it not been for the offender's mental illness".

He cited a 2014 Victorian case wherein a mother was convicted of infanticide of her six-week old baby girl and recklessly causing serious injury to the girl's twin sister. The court imposed a one-year community corrections order, saying: "No court could ever inflict a punishment on [the offender] more severe than that which this tragedy has itself imposed upon her and will continue to impose for many years, perhaps forever."

Mr Lange said his client had been charged with manslaughter, not infanticide, because she had a pre-existing mental illness exacerbated by the birth of her child. Mr Lange said that is "a distinction without a difference" and both offences carry a maximum term of 25 years in jail.

Crown prosecutor Mark Hobart, SC, said it was a "strange and difficult case" but the community might expect that she be sentenced to jail. He suggested any jail sentence could be suspended.

Mr Lange said that, if a jail sentence was imposed, it should be of such length that she is immediately released on parole.

The woman will be sentenced on May 19.