Can I mail in my application and pick up my Visa from Perth?

No, the China Consulate-general in Perth doesn't accept visa application by mail. You have to submit your application to the Consulate in person or entrust someone or a travel agency to submit on your behalf.
However, the visa application form should be fully filled in and signed by yourself (application for an applicant under 16 years old should be signed by one of his or her parents).