The information you have is HUGELY outdated.
CES stopped existing in the mid 90s. CES and DSS were merged into Centrelink, who manage all social welfare payments and still do engage in some jobseeking assistance. However the majority of jobseeker assistance (Training, job search & resume support and so on) is handled by external agencies.
There are different layers and rates of payments. “The Dole” as such doesn’t exist any more. There’s Youth Allowance, which is paid to people between the ages of 16-20 if they are studying and/or looking for work, or up to 24 years old if they’re currently engaged in an apprenticeship.
Newstart Allowance is “jobseekers allowance” for anyone over the age of 20. You are required to show proof of actively looking for work and you can be breached if you are offered a job and refuse to take it. This is problematic for people who are highly qualified, because you can be breached and cut off from benefits if you don’t apply for or refuse to accept a McJob if you’re offered it, even if you’re overqualified for that work.
Aged Pension is exactly what it sounds like.
Disability Pension is available for people who are diagnosed with a specific long-term illness that will cause them to be out of work for more than 2 years.
If you have a shorter term illness that will still require you to take an extended period of time off work, there is a Sickness Allowance that you can apply for as a stopgap solution. However it doesn’t pay as much as you’d earn at work in a lot of situations.
There is no such thing as a “Single Mothers’ Pension” any more. It’s the Sole Parent Pension, which is full support for a single parent (male or female) who is not working due to their requirements to look after their children. There are a range of child payments and tax breaks for working parents and/or partnered parents as well. But once your child is 16 (aka old enough to receive youth allowance) all of those payments cease.
There’s also a range of concessions for transport and utilities that are available to people on pensions. There are also other payments available to Aboriginals and Torres Strait islanders, as well as refugees and other “at risk” groups, as well as carers and the bereaved, widows and partners of people on support payments.