Australians are free to be a member of as many political parties as they choose.
However, members of the House of Representatives and senators can only belong to one political party at a time. They must resign from one before joining another. A recent example of this is Senator Cory Bernardi (South Australia), who resigned his membership of the Liberal Party in order to form a new party, the Australian Conservatives.
There are currently 57 federally registered political parties. Twelve of these parties have members who have been elected to the Australian Parliament.
You can find more information on political party membership at the Australian Electoral Commission.