Yes, Ms.Brenda, you can apply for visa to China in Australia.
the requirements for an L visa are as follows:
1. One completed Visa Application Form for People’s Republic of China with a passport photograph attached.
2. Your passport with at least 6-month validity and at least 2 blank visa pages and one photocopy of its photo page.
3. Applicants who have not been to mainland China should provide copies of photo page of their current passport as well as other ID, e.g. previous passport, driver license, etc. (Children under 16 are exempted).
4. If you have been granted Chinese visa(s) before, copies of recent Chinese visa with entry record is required.
5. Non-Australian passport holders, except for documents mentioned above, should provide valid Australian visa as well as entry record to the Consulate General (Original and the copy).