My passenger is flying from Uzbekistan to New Zealand and has to change planes in Australia. He has a work visa but no transit visa. Is this allowed? I know Russians cannot transit in Australia, but I'm not sure of the situation for Uzbekistan citizens.
This is actually rather simple. Australia has very well defined rules for transiting through without a visa. You can review the list of countries that this is allowed for on the Immigration Service site.
Once reviewed you can see that Uzbekistan is not one of the countries that transit is visa less unless the passenger is a holder of a diplomatic passport.