To work in South Korea you must obtain a work visa

South Korea has Working Holiday Agreements with Australia, Canada, Japan And New Zealand issuing visa that are valid for one year (12 months)

Requirements;

* Must a citizen of one of the above countries residing in that country at the time of application
* Intend primarily to holiday in the Republic of Korea and also to engage in employment as an incidental aspect of that holiday in order to supplement travel expenses
* Aged between 18 to 30 years
* Be without accompanying dependent
* Possess Return travel ticket and sufficient funds
* Have Touring schedule and touring activities
* Possess valid Passport

If granted a working holiday visa may not be employed as receptionist, dancer, singer, musician, acrobat etc. at places of entertainment which might endanger good morals and manners, or engage in types of business which go against the tenor of the agreement, such as provide medical treatment and other professions which require certain qualifications in accordance with domestic law.

There may be other requirements specific to the country you are applying in so if your unsure of the requirements its important to check with the nearest Embassy of Consulate of Korea.