Your kids will adjust fine (as in - faster than you! We moved 7 times before my kids were 10 - no big deal on any of them except the anxiety that happens before the first day of school) The key is to keep the kids busy - if they are bored, they are miserable - the second they have one friend, they are happy again.
There are lots of Australians in DXB (or were when we lived there). Compared to the US, Dubai is more expensive
Ocean Park (its better than the Disneyland over there - I would recommend not wasting time on Disneyland)
Big Buddha (its kitchy but my kids liked the tram car ride - get the one with the 'glass' bottom and the "village was nice enough). You can get to the trams via metro - stop at Tung Chung. If you are going to shop in HK (outside the street stalls) then you'd be better off doing it in Tung Chung as it is an outlet mall so is usually cheaper than everywhere else.
Go up the tram to Victoria Peak - we ate at Bubba Gump so we'd get the view- was nice enough and my kids liked the food.
There are a few museums in Kowloon that had some HK history - I forget which one my kids liked - but it was right at the tip closest to Hong Kong - it was on the water front.
If you go to Stanley and Stanley Market there is a Maritime museum my kids enjoyed. Also, good restaurants down there but I forget the names of them.
There are a billion places to hike in HK if you like hiking. Some are quite leisurely strolls and others are very hard. A leisurely one would be near HKIS in the Stanley area - near all the water reservoirs. Lantau had some amazing scenery.
There are lots of Malls and all that - not too much of a draw coming from Dubai - but a lot of good restaurants will be in the malls.
If you want to see the "markets" just have a guy take you to Wanchai. You can get all sorts of cheap Chinese toys (aka junk) and other stuff there.
Lots of people would recommend the Star Ferry - I didn't particularly enjoy that. I didn't like Disneyland because it pales in comparison to the other ones, Ocean Park is much better.
Oh, and I'd go ahead and get an octopus card first thing. The bus/metro system is excellent - prompt and very, very clean. The kids go at half (I think) fare if they have an octopus. That said, the only inexpensive thing in HK are the taxis so if you go that way it works too.
