What are some rebuttals I could use for the debate topic, "It's time for Australia to stop fighting other countries' wars"?

This all depends on how you regard Australia's international responsibilities.  Do you think that Australia has a responsibility in the Global War on Terror?  Should Australia fight the Islamic State, an organization that has the capacity to attack many nations, as it already has in America, Belgium, and France?  These are not "other people's wars," as many countries believe that they have some responsibility in fighting the Islamic State.  
What about Australia's foreign interests in terms of trade?  If a major trade partner with Australia, such as Japan or the United States, were attacked by a foreign nation, then it would sharply curtail the Australian economy.  While aid to a trade partner could be interpreted as Australia fighting "other people's wars," your side can look at it as Australia acting in its own interests in order to keep the Australian economy stable.  
Both of these arguments for internationalism have been used by other nations.  If you use this in your argument for Australia fighting "other people's wars," I think you should do well.