Do I need my certificate of freedom to marry stamped by the Thai embassy before getting married in Thailand?

Yes. You need to take your divorce paperwork to the embassy and pay to notarised it.

Then here's the guide

You will need the CNI and it will need to be translated to Thai. The translation needs to be done by anybody who is recognised by the ministry of foreign affairs as certified translator

Contact your embassy in Thailand. They know.

When I (Canadian) got married to a Thai, in Thailand, I had to get the 'free to marry' letter from the Canadian Consulate (Chiang Mai.)

I had to provide the consulate with evidence I was single (Canadian tax return, and late wife's death certificate) after which they wrote a letter verifying my status and stamped it with the Canadian Consulate Stamp, which I then brought to the the Amphur to get the marriage certificate (I don't think I had to get it translated, I don't recall exactly, as I was working toward the marriage visa and had a lot of other documents to deal with, some that needed to be translated & notarized and some that didn't.)

You are Australian, so I would think that the certificate you received from (I assume) the Australian government will serve to act as what my tax returns and death certificate did ... you should contact the Australian embassy/consulate in Thailand to see if they provide the service the Canadian consulate provided me (but I suspect if your certificate is an original, stamped, official document, it may be suitable for getting your marriage certificate, but I'm sure the people at the Amphur will have the final say and tell you what they are looking for.