As I understand it, the Australian student applies for and obtains a a Student Visa to Germany, and having arrived, obtains a student resident permit normally valid for 2 years and renewable ( Aufenthaltserlaubnis für Studienzwecke ).
Upon expiry of the permit and course of study, the student needs to Abmelden ( deregister ) from the community ( Einwohnermeldeamt, Bürgeramt or Ausländerbehörde ) and depart.
As an Australian, she can cross over to CH as a visitor, and re-enter Germany also as a visitor ( up to a certain number of days ) or alternatively apply for a Schengen Visa for longer visits.
If you are registered on our sister site
www.toytowngermany.com, you might be able to find relevant information and pose detailed questions especially about the German side of things.
EDIT:
One thread on TT. Another one
here. Please also refer to DAAD
here and the Residence Act ( Aufenthaltsgesetz )
here.