If the visa is an offshore visa (eg. Tourist visa, offshore General Skilled Migration visa, or Student visa), then there is no right of appeal. If it is an onshore visa, or if there is an onshore sponsor, then yes it may be appealed at the Migration Review Tribunal (MRT). The MRT is independent of the Department, and will overturn decisions if they are proved to be incorrect.
Jeff Harvie is a professional Migration Agent, registered with the Migration Agents Registration Authority, a statutory body set up by the Australian Government to regulate the standards of the profession, and to give protection to visa applicant clients.