For preschool children
There are lots of preschools. Chains include Kindercare, ABC. They have 2 or 3 rooms divided into under and over 2s, but the curriculum is divided 3 ways and so those with the room have under 2s, 2-3.5 and 3.5 to school age (which is your 5th birthday or the next school day after it).
Some include food, most don't and parents send a snack box. They are open long hours, some 7am until 6pm. Most open some variation of that start or finish to suit the local market.
A childminder here is called a home educator. You can have up to 4 chidren in your care and the parents pay you direct (about $4.50 per child), there is a Govt subsidy for preschool children and I think this gets spent on helping you get your home childproofed, giving you car seats and cots etc.
The Govt introduced 20 hours free ECE for age 3 and 4, though I missed all but a term of this so don't really know how it works.
Some children go to kindergarten which is much shorter hours (3 afternoons a week at 3. Five morning about 6 months before you start school). I don't think you can open a private kindergarten.
School Age
Most schools have an after school OSCAR programme from 3-5.30 or 6pm. Some schools have a before school programme. They take place in a building at the school or the library, but can be accessed by all of the local community. Some soft play places pick up by bus and run their own programme. Parents pay, but there are Govt subsidies if your income is under a certain level.
In the school holidays OSCAR run programmes during school hours, which involve trips out to the theatre, the swimming pool etc. There are by necessity a lot more of these than the after school programmes.
I have not come across a child minder who offers after school care. To do this you need a nanny it seems.