Mitcham woman Sofina Nikat, 22, is expected to face the Melbourne Magistrates Court on Wednesday after she was charged with one count of murder on Tuesday.
Nikat, wearing thongs and a dark coloured cardigan over her clothes, briefly faced an out-of-sessions court hearing on Tuesday night.
Detective Senior Sergeant Stuart Bailey told the short hearing Nikat had made "full admissions" in a police interview to killing her 14-month-old daughter Sanaya Sahib after she was arrested in Mont Albert on Tuesday morning.
Holding one hand to her face and holding a book in the other, Nikat was only required to speak when asked by the bail justice if she had been looked after in custody - quietly responding with "yeah, yeah".
Sanaya's body was found in the Darebin Creek on Sunday less than 24 hours after Nikat had told police her daughter had been snatched from her pram in a Heidelberg West park.
She told police a man, of African appearance smelling of alcohol and wearing no shoes, had pushed her to the ground before running off with the toddler.
The pair, from Mitcham, were staying with relatives in Heidelberg West after a separation between Nikat and Sanaya's father.
Nikat did not apply for bail and was remanded to appear at the Melbourne Magistrates Court on Wednesday.
