Do I need to have at least 6 months validity on my Australian passort if I will be staying in Korea for 2 days?
According to the Australian government's website on travel to Korea, the answer is yes - your passport must have six months validity from the date you plan to return to Australia, although there's no mention on the actual Korean sites as to how long your passport must be valid for to enter, just that it must be valid.
In general, the amount of time you plan on staying in a country doesn't affect requirements on how long your passport must be valid for. If a country states six months, it will be that regardless on how long you plan on staying. The alternative would be "valid until date of departure", which is obviously different.