As a current, financial member of the Australian Medical Association, you can use the post nominal letters AMA(M). 

You must agree to abide by the AMA Code of Ethics. The Code was updated in 2016 and can be viewed here. 

The right to use the post nominal letters has been included in the By Laws of Australian Medical Association Limited. The By Laws also provide for the award of a Fellowship of the AMA, where outstanding services have been provided to the Association.

If you wish to use AMA(M), place the post nominals letters after your existing post nominals. Post nominals to indicate voluntary membership of an association are generally listed after commonwealth honours and awards, academic qualifications and fellowships.