No, but you will need one of the following:
a) an Australian registered company; or
b) trading under a registered business name in any Australian State or Territory; or
c) an Australian partnership or sole trader; or
d) a foreign company licensed to trade in Australia; or
e) an owner of an Australian Registered Trade Mark; or
f) an applicant for an Australian Registered Trade Mark; or
g) an association incorporated in any Australian State or Territory; or
h) an Australian commercial statutory body.
Rules for .com.au names are set by auDA.org.au in Australia.