Are you asking about all-Qantas services or those involving codeshare or interline carriers? As best I can tell, carry-on allowances are not listed on the ticket and are only dependent on the rules of the operating carrier. Details for Qantas:
https://www.qantas.com/au/en/travel-info/baggage/carry-on-baggage.html
Note there are specific rules for Dash-8 services. From the T&C's I can't find any evidence that carry-on rules extend to connecting flights in the same way that checked baggage does, but would be curious to know if people have real-world examples.
Note that you can expect different rules for different operating carriers - this even applies for Jetstar flights (although gate agents may be lenient if you show you are on a connecting QF itinerary). I know people have gotten into trouble with this in the past by not checking their operating carrier's carry-on rules.