Australia has both undergraduate and graduate medical education programs. The undergraduate programs admit students after high school. Admission is based on grades and test scores. (UMAT/ISAT are required.) Graduate medical education admits students after the completion of an undergraduate degree in the chemical or biological sciences. Admission is based upon undergraduate grades and test scores. (GAMSAT or MCAT is required.)
Many Australian graduate medical programs readily accept international applicants if you meet entrance requirements–and can pay the approx AU$400K price tag. There is no financial aid available for international students.
Be aware that Australia has declared it has a physician oversupply. Physician was removed from the acceptable occupations category for immigration last year. Unless you already hold Australian citizenship or permanent resident status, you will not be placed into a clinical training program to become a general medicine physician. (Becoming a generalist is the first necessary step before specialization in psychiatry.)