Where do I obtain a certificate stating I am free to marry?

If you are in PRC, you can visit your embassy to acquire the certificate of No Impediment to Marriage. Before you go there, you should prepare these documents:
1. original completed CNI application form (downloaded from the embassy of Australian in PRC).
2. Your passport.
3. Your Chinese partner's ID card or passport.
4. an up to date certificate of single status. You can get it from the Registry of Births, Deaths and Marriages in Australia (If just turned 18 you are exempt from this).
5. divorce certificate if you got married once.
6. death certificate if your previous partner is dead.

If you submit the application in person, you can get it on the same day you submit it.