I know how it works if you are trying to find someone overseas because my ex should be using it to sort out the issues we have but he won't because the welfare of the child is it's main consideration and it won't force me to give him the children, all he could hope for is access, so he isn't interested.
For him to come over here and have a Hague Convention hearing, he would have to hire a solicitor in England and they would proceed from there.
Sooo you may have to hire a solicitor in Australia to impliment the Hague Convention. Now I do know that you can contact the state department and they will help you get a solicitor and help you through the process.
This might be a long shot but the London Attorney I used, very sparingly, is Australian but practices law in London. He is an international Family Law Solicitor. His name his Henry Brookman. He may not remember me because he only advised my Arkansas Attorneys back in 2005. It would be worth a call or e mail to his firm and he may be able to point you in the right direction.
http://www.brookman.co.uk/If that doesn't work, write me back and let me know, I have lots of info on the Hague Convention and I'm sure I can find something that might help you.
I am currently helping and English mother who is trying to sue her American ex for child support. He is living in the US now in Oregon and she is having trouble getting anything from him for their daughter. I am doing this as a friend because I'm no expert on the Hague Convention but after so many years of dealing with my ex ASSHOLE in the states, I have learned a LOT!
Let me know what happens.