In Australia can a woman with one kid easily get restraining order against her abusive husband? What type of proof she could be asked?

A history of calling the police... Material witnesses... The kid speaking up about what a prick his dad is... The real question is whether the woman is seeking to oppose the father's right to joint or partial custody.

yeah the best course is to find it out by yourself.

She should get a lawyer who will advise her.

A history of reporting the abuse to the police, health records where you have gone to the doctor/hospital, witnesses, photos of physical bruises, or mental abuse, even a diary of events.then report to the police and they will help

In Australia (and New Zealand)

Woman don't need to be abused. The laws are on their side.

Just like in the U.S. the mere accusation is enough to put the guy in jail. Until he can Prove his innocence.