Aussie electricity is supposed to be about 230V 50Hrz but generally anything rated 220-240V at 50Hrz will work ok.
Any electrical item you have should have a sticker on it that shows the power range it can handle....computers, laptops, and newer tv's usually always are able to handle the increased power....sometimes have to flip a switch on the back of computers first.
Most other common electronics will only accept 120V 60Hrz so in general I wouldnt bother bringing them.
You can get transformers that step the power down so that you can use those items but in general they use alot of electricity and unless a really solid build can lead to reduced life of your items and are fairly expensive especially if bought to run high power items.
Even with a transformer anything with a motor you really cant take as the US motors run at 60 Hrz so even if you use a transformer to convert the power the motor runs slower then its made to run and it will only get a fraction of its usual life before it dies.
Also the plugs are different so you have to buy plug converters or new power cords for anything your bringing over.
I am moving in July and plan to bring all my TV's and computers/laptops which all are able to handle the 230V power with just a cord change or adapter.
Also plan to bring my printer and stereo receiver that will need transformers to run.
Will not be bringing my Washer, Dryer, Fridge, Microwave, and small appliances due to them having motors or pulling so much juice that a transformer to handle them isnt ideal or cheap enough that bringing them and bothering with a transformer is just not economical.
Also keep in mind that electricity in Australia costs a lot more then it does here in the US so using a bunch of transformers that are not very efficient will cost more money per month as well.
Hope it helps!