Buying an American iPhone to use in Australia?

I currently live in Australia and was going to buy an iPhone but they are a lot cheaper in the US. If I was to buy an AT&T iPhone 4S for the US would it work here with my Vodafone simcard if I used this thing off ebay? Http://www.ebay.com/itm/190744232145
I don't wanna jailbreak it or do any of that crap.

Added (1). So buying a US iPhone to use in Australia permanently.

If it is unlocked to use All networks so you can use it in Australia.

You can buy an US GSM iPhone and definitely use it with Australian GSM SIM card after unlocking. I'm not sure with the method you have specified. But, I have unlocked my iPhone 4S safer and easier using remote unlocking service. I got the remote unlocking service for my iPhone 4S from http://www.simpleunlocking.com/apple-iphone-4s/rs16wp9/ at affordable cost with easy unlocking instructions. This method of unlocking doesn't require a jailbreak too. You too can try this method for unlocking your iPhone 4S.

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