I live in Australia and hold a M.A. degree...That degree doesn't exist in Australia
I started to wonder what Australia called an M.A., so I googled "MA Australia master of arts" and discovered Victoria University offering such degrees, e.g., https://www.vu.edu.au/courses/master-of-arts-hrat. So, it seems it does exist.
(The above previously appeared as a comment and the question has now been edited to add the following.)
I refer to a particular degree in the area of child education and not to the term 'Master of Arts', which of course does exist in Australia.
The particular name used by the awarding institute, the University of Hamburg, doesn't matter so much, the level of the qualification does.
What is the etiquette to present such a degree on a business card?
Use post-nominal letters, e.g.,
A. N. Other, M.A.