From http://www.legalaid.nsw.gov.au/publications/factsheets-and-resources

Are you experiencing domestic violence?

This brochure explains how Legal Aid NSW can help you if you are experiencing domestic or family violence.

Merit test

This looks at whether your case has a reasonable chance of success in court. The merit test does not apply to most domestic violence cases.

Can an ADVO defendant get legal aid?

The person an ADVO application is made against is called the defendant. A defendant in an ADVO application can only obtain a grant of legal aid in `exceptional circumstances.

While being gender neutral, it ignores the principle of innocence until proven guilty (by automatically believing alleged victims of domestic violence, and not believing the alleged perpetrator).

Here's the section on where to obtain legal help from:

Domestic violence services funded by Legal Aid NSW

Women’s Domestic Violence Court Advocacy Services (WDVCAS)

This service helps women and children to get information about domestic and family violence, and support women and children before, during and after the court process for obtaining an ADVO. You can contact your local WDVCAS by calling LawAccess NSW on 1300 888 529.

Domestic Violence Practitioner Scheme (DVPS)

These are lawyers paid by Legal Aid NSW who have expertise in domestic and family violence. They can help you with an ADVO matter and provide advice and referrals for other legal problems such as family law, victims compensation or debt. The DVPS only operates in some Local Courts. Contact your local WDVCAS or call LawAccess NSW on 1300 888 529 for more information.

The state government's domestic violence FAQ page also only lists these two services.

EDIT: I found the gender-neutral and help for men sections of the websites:

http://www.domesticviolence.nsw.gov.au/what_are_my_options/what_are_my_options/i_am_a_man_experiencing_domestic_violence

which is among gems such as "I am a young male and I am concerned about my behaviour in my relationship", and "Whether you are thinking about leaving your partner, have left your partner or plan to stay with him..." (in the "I have children" section).

And this site: http://www.lawassist.lawaccess.nsw.gov.au/lawassist/lawassist_avo.html