I don’t think she can get backdated child support because looking at the Family Court website, Department of Human Services and Legal Aid sites (eg, Legal Aid WA and Legal Aid Victoria) in relation to child support and child maintenance, you can recover arrears or late payments due under a child support/maintenance order, but it doesn’t appear that the Family Court or DHS will look at backdating an application before you were 18 and try to collect money that you believe should have been paid.
Even so, child support would have stopped when you were 18 (11 or so years ago now) which I imagine is well outside of the time to make an application.
Sorry, but I don’t think there is a claim/application to be made this many years after the time when an application would have been considered (when you were a child). At the time she was given full custody, I imagine there would have been some consideration of property and money settlement, I'm not sure why some kind of ongoing child support was not part of the deal. (Then again, I'm not a family lawyer, so there may be some differing views.) It sounds like your mother must have worked very hard to ensure your well being without child support from your father.