I agree with Flump. Almost all of the property in Sydney is unfurnished. You are therefore going to need a significant amount of money to set up home. I don't want to worry you, but Flump is right. If you are going in August, you need to book the flights right now. It's not exactly peak time, but even so, I've been to Aus three times and I've never seen a flight that didn't have every seat booked up.
You need to hire a car from the airport, I'm assuming. You will need to open bank accounts and credit cards, register with medicare.
You need to sit down and carefully itemise what you need to buy and what it's going to cost. You also need a short-term rental property (we had one for three weeks but had to extend it to five because we couldn't find a place to rent). Preferably one with some storage space like a garage, otherwise where will you put the furniture you buy?
You need a deposit for a flat and you need cash to buy a car and set up the internet (which is expensive).
We bought all second hand stuff and some new stuff from Ikea. the main things we bought were:-
Two cars (and then you need to register and insure them)
Fridge freezer, washer, TV, toaster, kettle, iron, phone, lamps, ironing board, TV table
Sofas, rugs, table and chairs, bed, bedside tables, cushions, cotbed, laundry baskets, side table, shelving unit, books, maps, baby changing mat, high chair, linen basket, steamer, microwave
Crockery, pans, cutlery, oven-ware, tupperware, glasses, cutlery tray, brushes, toilet brushes, towels, clock, toys, radio/CD player, patio table, BBQ, BBQ tools, coolbox, radiator, duvet, pillows, desk, printer, draining racks, clothes horse.
We brought £16,000 and we've spent it. It's a difficult thing to achieve, especially with a small child, so I think you should start planning!!!