PP our local childcare centre in Melbourne ran a government scheme called in-home care. We got one of their workers to come into our home to look after DD1 one-on-one. We were able to access this because DP was a shiftworker and we didn't need full days, just half days here and there. The way it worked was that we would let the centre know on the Friday before what hours we would need for the next week. There was a four-hour minimum block and the cost was something like $22 per hour but childcare benefit plus the childcare rebate applied (unlike for nannies).
I don't think it's very widespread but given that you live in a big city, I would think that a centre in Sydney would also run that scheme.
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