Just to clarify: The longest sector should determine what your allowance is for checked bags. This refers to the baggage rules for the longest individual flight in your itinerary.
In your case this means that connecting in the Middle East will result in the longest flight being Middle East to Australia (unless you add another stop). For connections in Asia, the Europe to Asia leg will probably be the longest.

For the carry-on allowance, it will be the operating carrier of each flight that sets the limits.