Does your friend know they can work while here on a student visa? Once their course has started they can work to 40 hrs a fortnight or maybe more, depending on their visa subclass. (See Permission to Work Arrangement for Student Visa Holders)
However, if they want to stay on after their course they’ll need a Working Holiday Visa
as you suggest and since they’re coming from Korea it’d be of Subclass 417
.
The Department of Immigration website lists following requirements (amongst others):
Now, I’m not an expert but it sounds to me like your friend would be ok so long as their work visa was applied for and granted before they arrived in Australia on their student visa.
To be sure, I’d suggest you/your friend spend some time checking the details online: http://www.immi.gov.au/immigration/
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