The woman, in her late 30s, is accused of drowning her daughter in the bathtub in her family's North Strathfield house here in November 2010, after months of obsessively worrying that the girl had dwarfism, the Sydney Morning Herald reported.
The court was told that soon after the baby was born in April 2010, she was tested for genetic abnormalities, including achondroplasia, the medical term for dwarfism, when the mother raised concerns about skin tags, a flat nose and the shape of her forehead.
Though the examinations cleared the baby of any condition, the mother remained highly anxious.
The Forensic tests on the woman's computer showed she searched the internet for terms including "drown", "infanticide", "smother" and "sudden infant death".
An autopsy found the baby had marks on the back of her head consistent with fingernail scratches.
On Friday, the Judge ordered the mother be detained in a facility determined by the Mental Health Review Tribunal, setting a limiting term, or maximum, of 20 years.