A mother who smothered her infant daughter before dumping her body in a creek in Melbourne's north-east has walked free from court after being sentenced to a 12-month community corrections order.

Sofina Nikat was suffering depression when she suffocated her 15-month-old, Sanaya Sahib, in a park in Heidelberg West in April last year.

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Nikat was initially charged with murder, but it was later downgraded to infanticide, which carries a maximum of five years in jail.

She pleaded guilty in September.

In sentencing, Justice Lex Lasry told the Victorian Supreme Court that Nikat's chances of rehabilitation were good, and a community corrections order was appropriate as she had already spent more than a year in prison.

"Your pre-sentence custody of 529 days is, on any view, a period long in excess of any sentence of imprisonment I would have considered imposing on you," he said.

Justice Lasry described the killing of Sanaya as a "tragedy for you and everyone connected with your family".

"The complexity of the mental state of some women after child birth and for some time thereafter is not to be underestimated, particularly when it is made more difficult by the surrounding circumstances which occurred in your case," he said.

Ms Sahib, left, said the family had fallen apart since the death of the child. ( ABC News: Emma Younger )

The court previously heard Nikat was living in a women's shelter at the time of the killing after separating from her husband, who she had wed in an arranged marriage.

Outside court, Detective Acting Inspector Stuart Bailey said the baby's father and grandfather were not able to attend court today due to the "emotional toll" Sanaya's death had taken on them.

Speaking on the family's behalf, Sanaya's aunt, Zahraa Sahib, said they were disappointed and upset by the outcome.

"We had no justice for her death," she said outside court.

"We were expecting something and it just completely failed us, and I don't think it's very fair that we've lost our little girl and there's nothing for her."

Ms Sahib said the family wanted Sanaya remembered as a "sweet little bubbly girl".

Flowers and stuffed toys left for dead child who was described as "sweet, bubbly." ( ABC News: James Hancock )

"We're just praying to God that this doesn't happen to anyone or anyone's family," she said.

The court heard the Fijian-born mother believed her daughter was "possessed" and "would be in a better place".

Nikat had initially told police a man of African appearance who smelt of alcohol had snatched her baby from her pram.

But she later confessed to the killing, telling detectives she "couldn't think straight" because she was "shocked that she really did that".

Defence barrister Christopher Dane QC had earlier told the court Nikat been a victim of domestic violence and was unable to cope living in a refuge with no financial or family support.