It might also help if you can give some clues as to whereabouts in Australia they went to, or whereabouts the seven children were born in Australia.
Betty is usually a shortened form of Elizabeth, so her death may be registered with that name. Did she marry, and if so what is her married surname? Is is specifically her death you are looking for?
Remember as crisane said, if any of these people are still living, you are not allowed to give their names.