I'd say about €12,000....but this is just my opinion..other posters may have thoughts on how you could make the trip for less.
Air fares from Dublin would be about €5,500, that would cover economy freedom fares which would be
a safer bet when travelling with very young children.
Accommodation in Bondi in a serviced apartment or short stay house let would be in the region of $200/$250 per night.
Spending money would have to include groceries, public transport, eating out, etc. so $200 a day would be a realistic budget. An example of public transport cost would be a multi day pass for the family ...around €50.
You also have travel insurance to consider...