We did Sydney, then Port Douglas, Ayers Rock, Perth, Singapore with a 2 year old. We are experienced travel bookers but the flights were so complicated, we left this to Trailfinders. We booked the accommodation directly and saved over £1,000 in doing so.
As others have commented, it is noticeably expensive, particularly in Sydney. Absolutely loved the Aquarium (I think this must be the best in the world), the ferry ride from Sydney to Manley was great fun, the Opera House tour was great too.
But by far the most amazing part for us was Port Douglas - the route from Cairns to Port Douglas is breathtaking and in Port Douglas you are between the Great Barrier Reef and the Daintree Rainforest - both World Heritage Sites. Go on car ferry across the Daintree, go on crocodile spotting tour, eat tropical ice creams at the ice cream farm en route, great animal farm in Port Douglas, beautiful beaches, snorkel/dive the Great Barrier Reef ...
Ayers Rock/Uluru - would recommend for max one or two nights as it is very very expensive and there isn't a great deal to do outside of Uluru Recommend the free of charge Rangers tour. An Aboriginal elder accompanied our ranger and so we were given a great insight into Aboriginal culture. Preferred Kata Tjuta as felt more desolate.
Only had a brief stopover in Perth - Fremantle is quite nice on a Sunday, nice fish restaurants but very busy on a Sunday.
Singapore was amazing for all sorts of reasons but the zoo is a must see - it was wow!