New visa rules: Dec 2007:
Under the new law, applicants for a new E2 visa or an extension have to submit their criminal background certificate and medical report. In addition, applicants are required to appear for a personal interview at the nearest Korean embassy or consulate in their home countries, with some exceptions such as, for example, mission location unreasonably distant from applicant's location. I'd say Australia qualifies as too distant from the USA. Go into the Sydney Korean Consulate, with all your documents, & fill out all the required forms.
(Criminal-check records are also required for C4 visa candidates who plan to work in English language camps here for less than 90 days.)
In their initial application package, prospective teachers must fill out a short, unofficial health statement regarding infectious diseases, drug use, and psychological problems. Then, within three months after arriving here, the official medical data must be provided to the immigration office, as part of the application for residence registration. The medical exam to be conducted by government-approved public and general hospitals includes tests for narcotics use and HIV/AIDS, the ministry explained.
The academic-credentials check has also been toughened. The original degree, along with a copy of it, must be submitted. The original will be returned after the credentials are authenticated. The copy must be verified by the Korean consulate in applicants' home countries or the Korean Council for University Education (www.kcue.or.kr).
For those whose credentials have already been authenticated by the KCUE, there is no need for the interview. They can apply for an E-2 visa at a Korean embassy in a third nation such as Japan. The Ministry of Justice has indicated that it will put those with verified academic credentials in its database so that they don't have to submit them again.
http://www.korea4expats.com/article-new-e2-visa-requirements-from-15-december-2007.html