An Australian woman, found guilty of killing her three-month-old daughter, has been spared a jail sentence after a court found out that she was suffering from postpartum depression when the incident occurred.

Melissa Arbuckle, 32, pleaded guilty to one count of infanticide over her daughter Lily's death at a train station in Melbourne last year. The woman killed her daughter by laying her down on train tracks. Arbuckle had also laid down beside her daughter in an attempt to kill herself.

The baby died hours after the incident while Arbuckle survived with fractures and internal bleeding. Arbuckle had taken Lily for or a walk on July 11 last year and had texted her husband to say that their daughter seemed unsettled, according to a report in The Independent.

The woman was later diagnosed with postpartum depression and psychosis, including auditory hallucinations, her lawyer told the court. "She had a fixed delusional belief she had harmed her child and they were both broken," Arbuckle's lawyer Megan Tittensor said.

"She had a perfectionist personality and need for control...she wanted to be the perfect mother. She had come to believe dying was her only option. She would hear voices telling her she was a bad mother," he added.

The Victorian Supreme Court released her on an adjourned undertaking for three years, which will allow her to live unsupervised, but she will need to make appearances before court.

Arbuckle, a well-respected vet, had no prior criminal history or mental health concerns before her daughter was killed, heard the court.

"The fact that the severity of your postpartum depression was overlooked is an unfortunate feature that this case has in common with certain other cases of infanticide," said Justice Jane Dixon.

"She seems very much aware of the incredible suffering her actions have caused," Justice Dixon told the court. She added that it was "extremely unlikely" Arbuckle would re-offend.

Postpartum Depression Lasts 3 Years
Postpartum depression can last up to 3 years. Photo: Pixabay