The most common and most likely answer to this crossword clue is the 4 letter word EMEU
E
M
E
U
More clues leading to the result EMEU
Buddy explains!

The straight part
We know that "fast Aussie bird" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fast aussie bird = emeu.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.