Australian citizen on holiday in Germany wanting to get a Chinese visa?

You can try to apply for a Chinese tourist visa from China Embassy in Berlin, however, I can't sure you can get it, at present, the visa application in a third country varies from country to country. Some Chinese embassies/consulates ask applicants to provide the residence permit or work permit of the country if they apply visa in the country other than the country of their current nationality. Maybe your application will be denied because you can't provide German residence permit or work permit.