August in SYD will be cool to cold in the evenings (well, my definition of cold anyway given our winter is very tame compared to Northern winters!) but the days should be fine - good for light sweater type clothing.
SIN-SYD may be very hard to get on given the European summer vacation traffic and SIN being a major hub between SE Asia/Sth Pac and Europe. Just have lot's of backups planned - QF in particular often has it's own staff backed up in SIN for days on end in peak periods.

One thing I've noticed is you have one heck of a lot of travelling crammed into a very short space of time. Everyone knows we live at the rear end of the earth and it's a long way down here, but people just don't realise exactly how far it really is until they get off the flights. If you have young ones with you, you will need to plan a day or two of adjustment to time zones and certainly to combat jet-lag. This will impact on your leisure and itinerary time. Whilst it may be a once in a lifetime thing for many, it's such a long way to get here and such a big place to see, one has to weigh seeing as much as one can in very limited time against length of time planned.