The three young children are in state care and their parents have appealed against a children's court order that they be immunised.

On Wednesday the parents took their fight to the Supreme Court, where Victoria Legal Aid acted on their behalf.

Health and state government officials fear that if successful, the appeal could set what they say is a dangerous precedent for children in state care, and undermine their message that vaccination saves lives.

Lawyers for the state government also argue courts are bound to make decisions that are in the best interests of children.

It is understood the three children at the centre of the legal fight, who cannot be identified, are in state care over concerns about their welfare.

On Wednesday the father told Justice Robert Osborn that there's "more chance of being bitten by a dog than getting measles".

"There's not much chance of getting measles," the father said.

"There are more shark deaths than there are from measles,"

The father said he and his partner opposed "putting something into our [bodies] that we can't control" and that he spent time in hospital as a child with measles but had developed a natural immunity.

"I am just trying to do the best thing for our kids, I believe this is best thing for our kids," he said.

Earlier, John McLoughlin, acting for the parents, told Justice Osborn the appeal was not about the merits of vaccination, but whether a court could make a long-term ruling for a child that was permanent and irreversible.

He said the children were away from their parents on a temporary basis, yet the children's court magistrate ordered a long-term provision. It is unclear how long the children will be in state care.

But Ian Freckleton, QC, for the Department of Health and Human Services, said the department was limited in its powers on issues such as vaccination, to guard against excessive use of power by the state.

In contrast, he said, courts were bound to make rulings that were in the best interest of children. The magistrate had adopted this path in his ruling, he said.

Dr Freckleton said the children's court system would be unworkable if it was prevented from making broad orders over children's welfare.

During submissions, Justice Osborn put hypothetical scenarios to Mr McLoughlin, asking what would happen if there were no safeguards for children who cut themselves on rusty metal, lived in small communities when infectious diseases hit, or endured seizures and weren't medicated.

Mr McLoughlin said the department had the power to act in emergency situations, but the judge replied: "Why would you ... leave it to the [department] secretary to anticipate when there's an outbreak of some infectious disease in rural Victoria?"

Victoria Legal Aid said earlier on Wednesday it wasn't taking a position on immunisation, but was focused on testing the power of the children's court in allowing the government to make a long-term decision about a child.

The state government cannot block the appeal as Victoria Legal Aid is an independent body.

Health Minister Jill Hennessy told radio station 3AW the legal aid-funded challenge was a disappointing use of public funds when health experts were battling to promote vaccination.

"I'd be very disappointed if other resources were being utilised in support of those that are opposed to vaccination, but there are independent processes about who gets legal aid and for what," she said.

Justice Osborn said he hoped to rule on the matter before Christmas.