Australian citizen w/ Canadian work visa expiring soon, traveling with a stopover in Kunming

Your college must be refused travel on other grounds or due to the airline's wrong interpretation of the rules. Canada's entry policy on work permit holders is that they only need to board the flight with an eTA or a temporary resident visa (TRV) and nothing else, and inspection of their work permit is done after arrival with a CBSA officer if required. Some airlines have, however, erroneously refused boarding to those whose TRV is on their old passport, although this is very rare.

With you being an Australian citizen (and therefore only needs an eTA) you only need to make sure that your current passport is linked to an eTA at the time of boarding. Your work permit is the one that decides how long you can remain in Canada. Similarly, if you don't have an eTA at the time of check-in, then you won't be allowed to travel even when your work permit is still valid.