90 day holiday visa for South Korea

What you're asking about is called a visa run. Staying on back-to-back tourist visas is frowned on by many countries, and Immigration will probably start wondering if you're working illegally sooner or later, but anecdotal evidence says South Korea is not particularly picky and it's possible to stay for years this way. Your mileage may vary.

However, it would probably be cheaper, safer and easier to apply for a regular 90-day tourist visa, which can be extended by another 90 days:

Citizens from a country excluded from the Visa Exemption Agreement but granted visa-free entry and intending to stay in the country for 30 days or more must apply for a visa. ... Those from Australia can stay up to 90 days. ... Applicants may be asked to submit additional documents if required for examination. Furthermore, visas may be extended for up to 90 days. All visas, including long-term visas, are for a single visit (single-entry visa).

The anecdotal source above also claims it's possible to extend a visa-free entry, but I can't find official confirmation of this.

All that said, if you're planning on moving to Korea for a longer period, have you considered working there legally? If you're a native English speaker, it's fairly easy to find employment at a hagwon school as an English teacher, and they'll sort out your visa too.