There's 24 hour shopping at some of the big shopping malls on the outskirts of the city. Of course there's always, Crown in the city. There will be no public transport on the 25 and 26 Dec as it's a public holiday and most shops except for Chinese eateries will be closed all over the city and suburbs. Thus my advise rent a car when you arrive. You can drive the car to Tasmania (just tell the rental company) via car ferries. Taxis are very expensive and very difficult to get.
Have a great time.