There are various Centrelink payments for which she may have been eligible at the time, including Jobseeker Payment, Disability Support Pension, Parenting Payment and Families
Payment. Please note that "eligibility" relates to whether or not someone satisfies the relevant legislative criteria as opposed to "entitlement".
(Eg for someone to be eligible to receive Jobseeker Payment, they would need to be aged between 22 and Age Pension age, and looking for work, or temporarily sick or injured, and unable to do their usual work. Australian Residency is also a legislative requirement.
Someone may satisfy the legislative requirements for a specific payment, but may have no "entitlement" due to their income. This relates to the rate of payment.
Many recipients have income which fluctuates - which may have the effect of their payment rate also fluctuating.
(Most Australian Websleuthers would have heard about the "Robodebt" situation whereby unlawful debts were raised against many pensioners, due to flawed assessment of (mainly) fluctuating incomes.)
Regarding Child Support, IMO it is likely that SP was paying Child Support (there are exceptions, but I doubt that they would apply in this case.)
See below for information regarding the Child Support payment formula (this is the "simple" version.) (gasp)
Watch and comment in YouTube To learn how child support is calculated in Australia (how it works), check out the infographic and discussion below. To estimate your child support payments, use the calculator / estimator (it's cleaner than
childsupportaustralia.com