I live in Sydney, but have travelled widely in the past. One warning: when you've travelled abroad once and have enjoyed the experience, you'll find that you can't get enough of it!
You've chosen a good route! In Vancouver, don't fail to visit the Capiliano suspension bridge. Also, the US border is less than 100 kilometres away. You might consider a side trip into Washington State, just to add another country's immigration stamp to your passport.
Sydney? I may not be a good guide here. As a native Sydneyite I probably don't fully appreciate the treasures on my own doorstep, but make sure your friends at least take you on one trip to see the Blue Mountains behind the city. A day trip to Canberra might also be in order. Word of warning - when you get to one of our celebrated surfing beaches, don't fail to smear on the sun block.
After Sydney, you might find Melbourne a little disappointing. It isn't as picturesque, it lacks surfing beaches on its front doorstep and is generally regarded as more conservative than Sydney... but you must discover it for yourself. In any case, here are four places of interest you can look into: Phillip Island fairy penguin parade; the Yarra Valley wineries (some of the best in Australia); Daylesford Spa in central Victoria and the spectacular coast road between Geelong and Port Campbell (with views of the Twelve Apostles rock formations en route).
Cairns? Definitely take a glass bottomed boat out to Green Island - a real coral island on the Great Barrier Reef - and view the living coral in all its brilliant colours. Be warned though: October to April is the tropical wet season there and it gets very humid!
Uluru - lucky you! The surrounding region, with its clear desert air and splendid rock colours, is really something. I hope you find the local Aboriginal culture interesting; the indigenous Australian culture and way of life is the oldest on Earth. Europeans characteristically think of Australia as "young" and their own countries as "old", but consider it from an Aboriginal point of view and you get a totally different picture.
Good luck, Milly, and enjoy your travels. Hope this has been of help!
