I live in Adelaide and want to apply for a Z visa.

You should apply for the China visa from the Embassy of China in Canberra. If you can't go to the embassy in person, you may submit your application by email. However, the Embassy strongly recommends that all visa applications be made in person (either by yourself, a friend or via a travel agent) in case of unforeseeable inconveniences incurred during mail-delivery. The Embassy is not responsible for any loss, damage or delay of your passports/documents during mail-delivery.

It seems that no health check form is required by the China Embassy in Canberra for the China work visa application.