Arthur Freeman threw his four-year-old daughter Darcey to her death off Melbourne's West Gate Bridge shortly after crying to a friend that he had lost his children.
As he drove over the bridge on what was supposed to be Darcey's first day of school, Freeman stopped his car, turned on the hazard lights and pulled her onto the rail before throwing her 58 metres into the Yarra River below.
Her murder, on January 29, 2009, came the day after a court made final orders in a long-running custody battle between Freeman and his former wife Peta Barnes.
More than six years later, the Victorian Coroner's Court is trying to determine whether the legal and child protection systems failed little Darcey.
Ms Barnes had raised concerns about Freeman's behaviour during GP visits in the years leading up to Darcey's death, the inquest heard on Wednesday.
Ms Barnes told one doctor she feared Freeman would harm her children, but her concerns were not reported to child protection authorities.
It is only mandatory for a GP to report to child protection if they believe the child is in significant danger.
Freeman had attended a number of GP appointments with his children who did not appear distressed or show signs of physical harm, the court heard.
Ms Barnes took the stand briefly to praise authorities who dealt with the aftermath of the tragedy.
"Their dedication, compassion and skill needs to be acknowledged and recognised," she said.
Senior Sergeant Damian Jackson, who investigated Darcey's death, was an exemplary individual whose management of the horrendous case was sensitive, responsive and caring, she said.
Snr Sgt Jackson told the inquest Freeman was driving erratically before he stopped on the bridge.
There Freeman phoned a friend and spoke of having "lost his children" before throwing Darcey from the bridge.
When Ms Barnes called Freeman from Darcey's school that morning to ask where she was, he said: "Say goodbye to your children".
Freeman's two other children, who cannot be named, were still inside the car and one of them urged him to help Darcey after he threw her from the bridge.
"He asked his father repeatedly to go back and get Darcey ... because she couldn't swim," Snr Sgt Jackson said.
Freeman believed a family report compiled by a clinical psychologist had contributed to his diminished custody rights, Snr Sgt Jackson said.
Freeman has been jailed for life with a 32-year minimum for Darcey's murder.
State coroner Ian Gray will consider whether GPs have a thorough understanding of mandatory child abuse reporting requirements and whether there is co-operation between doctors and the Department of Human Services.
He will also examine why lawyers are not subject to mandatory child abuse reporting and whether they are adequately trained.
The inquest comes during the first week of public hearings in the Victorian government's Australian-first royal commission into family violence.
