Sure the WHO needs to be called to account for stuff-ups just like any other organization but just by reading your post, you seem to have a hangup on China. Yes, the Chinese government is dictatorial and I dislike that type of government, however, just about all governments have their plusses and minuses with the main minus being "greed" within the ruling party. Of course, it does not help when ideology (religious and political) takes centre stage as well, which throughout history has resulted in much misery for our species.
Response by WHO to COVID-19 is here with the earliest date being 31st Dec 2019. Sure you could say that was late but that would be the Chinese governments' fault for not reporting sooner. Granted that WHO did not declare the virus a pandemic until the 30th Jan 2020 although the first death in China was on the 11th Jan 2020, however, the alarm bells were already ringing and many governments chose to ignore the potential problem.
Italy has a population of about 60 million with a death toll due to the COVID-19 virus of about 33,229 and counting. You are correct in that Australia and New Zealand don't have anywhere near the amount of international travel that Europe and the USA have although most of our population is concentrated in a few cities. Fortunately, we have a very low death rate although we do have testing, social distancing and contract tracing in place. In addition, we also have quite a good health care system.
As to the Australian Government being owned by China. Australia (pop 24.99 million, landmass 7.692 million sq km) has a small population compared to China (pop 1.393 billion, landmass 9.597 million sq km) so our government has to be diplomatic since we do have trade relations. The same applies to many countries around the world including the US and Europe.
Because our Primeminster has supported the investigation into the COVID-19 virus relations have soured with China but because successive Australian governments after WW2 have basically followed US dictates we are now in a quandary as to how to approach China since the US government is not helping. Sure you could argue that China has a communist dictatorial government but like it or not they are approaching superpower status and have to be approached by diplomatic means since war would be catastrophic for all countries involved and even those not involved.