Australia has a tax treaty with South Korea. I am not sure on all the technical details but I will try to summarise. If you are an Australian resident and you give your employer in South Korea a letter of Australian residency from the ATO you won’t pay any tax in Korea but you will have to lodge a tax return back in Australia. If you are lazy and don’t give your employer a letter of Australian residency you will be taxed in Korea AND in Australia. Yes, you read that right. Tax will be taken out of your pay in Korea and you will still have to lodge a tax return in Australia. On your Australian tax return I think you can claim the tax paid in Korea so in the long run you wouldn’t be any worse off, but it would mean you have less money in your monthly pay packet.
Non Australian Residents
If you are not considered an Australian resident you don’t have to pay any tax to Australia on money you earn in Korea. HOWEVER, if you have investments or savings in Australia you will have to lodge a tax return in Australia and pay tax (at a significantly higher rate) on any income generated from those investments.