The 35-year-old man, who cannot be named because that could identify the victim, woke to the sound of the child crying and found her on the bathroom floor.

He pleaded guilty in the online division of the Warrnambool Magistrates Court on Wednesday to leaving a child without supervision and action resulting in harm to a child.

The court heard the child suffered "significant bruising" to her head, ear and chin.

The incident happened in January 2019 and was reported to police and the Department of Health and Human Services after a witness observed the child's injuries, took photographs and sent them to the authorities.

The court heard the man spoke to a detective from the Warrnambool police Sexual Offences and Child Abuse Investigation Team (SOCIT) on January 17 last year and agreed to take his daughter to the South West Healthcare emergency department but never showed.

The father made no attempt to take his daughter to hospital and ignored numerous phone calls from the witness, police and DHHS.

He was located at a property in south-east Melbourne the following day.

The child was removed from his care and presented to the Monash Children's Hospital.

The man was interviewed at Warrnambool police station on April 4.

He told police he was showering with the victim before getting out, putting the plug in the bath and leaving his daughter in "about an inch or so" of water.

He then went downstairs, had a beer and fell asleep on the couch.

The man told police he woke to the sound of his daughter crying but did not believe she was injured or bruised.

The man was convicted, fined $2000 and ordered to be of good behaviour for 18 months.

Lawyer Morgan Adams said the offending was a profound example of poor parenting.

"To leave a child in the bath, go downstairs, pour yourself a beer and go to bed - it's a set of circumstances that are so far from ideal that they are appropriately seen as criminal," he said.

"Parents make mistakes all the time but this is not a mistake, this is criminal."

But, the lawyer said his client had shown "profound remorse" for the offending, which he said had "significant, permanent and long-lasting effects on him".

He said the child was now in the foster care system.

"The risk of this reoccurring is pretty much non-existent given there is no longer any children in his care," Mr Adams said.

Magistrate Simon Guthrie said his greatest concern was the man's refusal to take the child to the doctor.

"He didn't take the child to the doctors at that time and the fact he left a child in an inch or so of water, children drown in that sort of thing, we know that for a fact," he said.

"That is a concern to me.

"I was horrified at first instance... Had there been any further incidents, I would have jailed you."

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