A suspected criminal is a suspected criminal; I don't know what the tradition is in Oz, but wouldn't they vote (present a majority) to nullify any diplomatic immunity?
I know about cases in parliamentary democracies where someone's immunity has been nullified - assuming they have it in Australia - but only in domestic disputes, not international.
Australia does not have immunity for Parliamentarians.
Immunity is mostly a feature of countries with fully separated powers.
In fused Parliamentary systems it makes less sense to worry about the infringements of the Executive upon the Legislative, because the Executive is subsidiary to the Legislative.
I know about cases in parliamentary democracies where someone's immunity has been nullified - assuming they have it in Australia - but only in domestic disputes, not international.