I did a similar holiday at Christmas and spent 3 nights/4 days in Sydney. It was wonderful. I think I could have done with another couple of days but that would have been about it - I never got to see any of the museums because the kids always wanted to do or go somewhere else. I would have loved to have spent longer in the Blue Mountains, we loved Scenic World but didn't get enough hours there at all (but we went on organised trip).
We caught the James Cook ferry to Manly and bought the 24 hour hop on hop off ticket, so used it on the Saturday afternoon to pop over to the zoo, and then on Sunday to pop over to Manly, and they weren't that strict about checking the times on the way back so we managed to get the boat back without having to pay.
I actually liked the James Cook boats because you got a guided tour around the harbour whichever direction you went in, so I found them really interesting.
But I do think about a week in Sydney would be long enough, it's a pretty small city.
I didn't get to do Uluru which I would also have liked to do, there are were flights there from Sydney and from Adelaide where we spent the majority of the holiday. But, it means I'm just going to have to go back to Australia to visit.
Have a lovely visit. For myself I didn't find the flight too bad, but my DS1 decided to spend the whole 15 hour leg from KL to Heathrow throwing up with air sickness. That was a bloody nightmare for me and the poor sods sat near us.