Doctors were warned Arthur Freeman was violent but did not report him to authorities before he threw his daughter Darcey from Melbourne's West Gate Bridge, an inquest has heard.

The Victorian Coroners Court is investigating whether improvements could be made to better protect children in the wake of Darcey Freeman's murder.

Darcey died when she was thrown from the bridge by her father on January 29, 2009, in front of her two young brothers and shocked witnesses.

Freeman was supposed to be driving Darcey to her first day of school.

In 2011 he was sentenced to 32 years in prison for Darcey's murder.

The court was read statements today from two different doctors who said they had been told Freeman was violent.

"I saw [Darcey's mother] Peta Barnes on 13 April 2007 and she disclosed problems with her angry, irrational husband who shoves and pushes her and is often angry at the kids," one doctor's statement said.

The other doctor said Ms Barnes revealed she was concerned about Freeman's violent behaviour and "expressed fear he [Freeman] would harm her children".

There are mandatory reporting obligations for Victorian doctors who are told of suspected child abuse.

However, Professor Kelsey Hegarty from the Royal Australian College of General Practitioners (RACGP) told the court the reporting requirements were subjective and neither doctor acted inappropriately.

Both doctors said in their statements that Ms Barnes was dealing with a lawyer and police who they assumed were best placed to report the concerns.

"When they see that lawyers are involved or police are involved, they often think that safety issues are being taken care of," Professor Hegarty said outside court.

Mandatory family violence training recommended

Professor Hegarty told coroner Ian Gray that many GPs were not aware of what to do when someone reported family violence.

She called for mandatory family violence training for all GPs but said that position was not supported by the RACGP.

Darcey Freeman was thrown from the West Gate Bridge on what was supposed to be her first day of school. ( AAP )

"I'm advocating that every GP should have mandatory training in child safe guarding where they learn to assess the risk for children," she said outside court.

Professor Hegarty also called for a Medicare-funded "family safety plan" similar to mental health plans.

"I'd like to see a family safety plan where GPs could spend half an hour really assessing a family's risk, then referring onto experts in the area, as we do with mental health plans referring on to psychologists."

In a brief statement read to the coroner, Ms Barnes commended the work of the water police who found her daughter's body.

"Nothing more could be asked for from any of them," she said.

"They went beyond the call of duty, they remain the unsung heroes of our community."

She called for the lead police investigator Senior Sergeant Jackson to be given an award by Victoria Police, saying he played an "exemplary role".

She also praised the staff at the Royal Children's Hospital for "their dedication, compassion and skill".

Arthur Freeman upset over custody battle, inquest hears

The morning he threw Darcey off the West Gate Bridge, Freeman called a friend in tears about losing a custody battle, the inquest heard.

Senior Sergeant Damian Jackson told the inquest Freeman had never provided an account of what happened that morning.

The day before Darcey's death, after a long custody dispute, a court had reduced Freeman's access to Darcey, the inquiry was told.

The court was told Freeman was angry and upset about the decision and on the morning of his daughter's death he called a friend in tears.