In the NSW Supreme Court in Sydney on Thursday, Acting Justice Jane Mathews began hearing sentencing submissions in relation to the woman.
Prosecutor Chris Maxwell QC told the court the woman had pleaded guilty at a local court to the manslaughter of the baby girl, who died in July 2004.
"The post mortem indicated the child had a blunt force injury to the head and there was a skull fracture," he said.
The woman also had pleaded guilty to acting with intent to pervert the course of justice by claiming another person had confessed to killing the baby.
According to an agreed statement of facts tendered to the judge, the woman admitted in her fourth interview with police to harming the baby.
She said she had been extremely tired and "very stressed out and hanging out from the drugs" and had put the baby down too hard on the bed.
The hearing continues.