Realpolitik. One's largest export destination (by far), and quite likely these days largest foreign investor, does carry a certain sway, and a considerable vested interest, in domestic politics and foreign affairs. Lobbying and influence peddling necessarily follows.
Given Australia's pronounced pro-US and anti-China (plus anyone else who the USA is anti) stance in foreign affairs, I have to say their influence thus far has been pretty benign really. But how long might this last? Plain fact is, China has enormous economic clout with Australia- it could send the nation bankrupt.