Well I don't really know what the rules are over there, but here you're entitled to centrelink payments until the child reaches majority. There has recently been new legislation which requires sole parents to look for part time work once their kids start school, but I think most responsible, non system abusing parents do that anyway. Another option is to go into vocational training or higher education which is what I did when I found myself as a single parent with two little kids. That worked for me as it does many other single parents.

Another thing is that the parent who doesn't live with the kids is meant to pay child support, so depending on the level of support they're providing financially, there'll be a greater or lesser amount paid by centrelink.