So said Sofina Nikat to her daughter in April last year, reflecting her frustration at caring for a demanding infant, and the desperation of her own sad life.

Little Sanaya Sahib couldn't respond. She was 15 months old, often crying, waking regularly at night. At the begining of the month she'd had a seizure.

On April 9, Sanaya was crying again and her mother put her in the stroller and walked to nearby Olympic Park. It should have been a peaceful walk for a grizzly girl.

But Nikat was alone when she returned 30 minutes later to her cousin's Heidelberg West home. Her daughter's body had been left in Darebin Creek.

On Friday, Nikat marked her 24th birthday by pleading guilty to infanticide in the Supreme Court. She spent most of the following two hours with her head down, particularly when CCTV vision of her walk through the park was played.

Sanaya's disappearance prompted a large police search, after Nikat reported her daughter was snatched by a barefoot man of African appearance who smelt of alcohol.

Early the following day, Sanaya's body was found. She had been smothered before Nikat rolled her body into the water.

Nikat confessed two days later and was charged with murder. She was committed to trial on that charge in March, until prosecutors accepted she was mentally disturbed when she killed her daughter, and withdrew the more serious charge.

Infanticide, which carries a maximum penalty of five years in jail, applies to women who kill their biological child, where the woman is affected by a mental-health problem related to childbirth. It only applies when the victim is under two.

Sameer Sahib spoke of feeling "robbed" at never seeing his daughter go to kindergarten, school, own her own car and get married.

"When I found out who had really done that I broke down. I couldn't understand how a mother could do that to their own child," Mr Sahib said in a victim impact statement.

But defence counsel Christopher Dane, QC, said this "exceedingly sad case" needed explaining to be understood by the community.

Nikat came to Australia from her native Fiji under an arranged marriage but, Mr Dane said, was the victim of domestic abuse and criticised by her in-laws for her housekeeping failings.

Six months after Sanaya's birth, Nikat and Mr Sahib separated, and the mother and daughter spent time in a women's refuge before a final stint at her cousin's home.

Mr Dane said Nikat was socially isolated, vulnerable and developed a major depressive disorder. When she told her parents in Fiji about Sanaya's troubles, they went to an imam, who found the infant was possessed by an "evil spirit".

Only holy water could cleanse the spirit, the imam claimed.

Mr Dane said Nikat's false claims about the kidnapper illustrated her "florid and irrational" state.

"The balance of her mind was disturbed when this act took place," he said.

The defence lawyer called for Nikat to serve a one-year community corrections order without jail, after 529 days already served in custody.

He would have applied for bail much earlier, he said, but she had "nowhere to go". Justice Lex Lasry granted bail.

Of the five women to have pleaded guilty previously to infanticide in Victoria, only Akon Guode was jailed on the charge.

Guode was jailed for 12 months as part of an overall term of 26 years and six months for drowning three of her children by driving into a Wyndham Vale lake in April 2015. She also pleaded guilty to two counts of murder.

Justice Lasry, who jailed Guode in May, said Nikat's appeared to be a "classic case" of infanticide.

Prosecutor Kerri Judd, QC, said a comunity order was inappropriate, as Nikat had been reluctant to accept responsibility and declined previous offers of help.

"Infanticide is not a justification for killing, it remains a criminal offence ... and others must be deterred. The killing of Sanaya must be denounced," Ms Judd said.

Nikat will be sentenced at a later date.

Woman who have pleaded guilty to infanticide

• Leanne Azzopardi Drowned five-week-old daughter Hayley in the bathtub in 2003. Spared jail by a Supreme Court judge and put on an 18-month community corrections order (CCO).
• Lauren Curnow Beat her baby son after giving birth alone at home in 2004. Spared jail and put on a three-year good behaviour bond.
• QPX (name suppressed) Inflicted numerous bone fractures on her twin daughters in 2012. One died at eight weeks and the other survived, but suffered serious injuries. Pleaded guilty to infanticide and recklessly causing serious injury. Spared jail and put on a one-year CCO.
• ZZMM (name suppressed) Smothered her newborn daughter in the moments after she gave birth alone at home in 2014, and left the baby's body under a tree. Spared jail and put on a one-year CCO.
• Akon Guode Drove her car into a lake in 2015, drowning three of the four children inside. Pleaded guilty to two murder charges and single counts of infanticide and attempted murder. Jailed for 12 months on the infanticide charge, as part of an overall sentence of 26 years and six months.

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