I've done 2 weeks in Australia a couple of times. I got mildly told of going through security / immigration on the way out because I had "not stayed long enough".
You used to be able to buy discounted tickets for internal flights as long as you bought them outside Oz.
I would say for two weeks Sydney and Cairns would be a good mix. Sydney for the opera house (see something) museums, arts, jewellery (you have to come back with an opal or two).
Cairns is in the North and there are trips to the barrier reef, the rainforest and a few other things, I think I fed some kangaroos and met a couple of crocodiles.
Perth has lots of art galleries, independent artists but you really need a car to get to them. But you could do Freeo (Freemantle) and Rottnest Island where you can fall in love with a quokka. I did a whole day motorbike tour, you can either ride a hire bike or go on the back of a guide's bike.
Go cuddle a Koala at a wildlife park (they are not native to WA so you don't see them in the wild).
Oh and if you go on a wine river tour it is nothing like you get in Europe. As soon as you are on the boat they offer you a drink, at this point take coffee or juice, you need to pace yourself.
You will see a couple of vineyards, be fed and sample some wine, quite a lot of wine.
On the way back the boat will pass a rival company going in the other direction so you have to (well you are not forced but encouraged) to get up and dance and convince the other boat's passengers you are having more fun than them.