To become a computer engineer you usually have to study electronic, computer, computer systems or software engineering at university. To get into these courses you usually need to gain your Senior Secondary Certificate of Education. Prerequisite subjects, or assumed knowledge, in one or more of English, mathematics, chemistry and physics are normally required.
A number of universities in Australia offer degrees in these areas. Universities have different prerequisites and some have flexible entry requirements or offer external study. Contact the institutions you are interested in for more information.
Given the full range of degrees that can be accessed for those wishing to become computer engineers, what they do is extremely broad. There is no one answer here, due to the fact that a computer engineer performs tasks pertaining to their specific skillset.
Software engineers, for example, dabble in programming and app development compared to the maintenance of computers that hardware engineers perform. On another scale, the network engineers out there design the systems that the hardware engineers maintain. It's a full circle industry with many different avenues.