It's Australian dollar and not Australian Dollar, It's Indian rupee and not Indian Rupee, it's Japanese yen and not Japanese Yen and so on.
I know that…
Proper nouns are capitalized.
Aren't they all proper nouns since we are specifically using that name of currency for that country only?
If you say that it's not capitalized as 'dollar' is used for many other countries' currencies and so 'rupee', what about the currency name 'cedi' which only the country of Ghana has for its currency?
In that special case where cedi should mean the currency of Ghana and only Ghana, it's still not Ghana Cedi.
Best Answer
Don't think of Australian dollar as a single proper noun. Instead, think of it as a combination of two words, meaning "a dollar that happens to be Australian":
There are lots of kinds of dollars, and we use adjectives like Australian and Canadian to say which sort we're talking about more specifically. There are lots of kinds of rupees, too, and we use adjectives like Indian or Indonesian to specify which sort we mean. Something similar is true of the Japanese yen and Chinese yuan (which are, by the way, etymologically the same word).
Note that in the preceding paragraph I talked about kinds of dollars and kinds of rupees. I didn't just say dollars and rupees, because an individual dollar is a piece of currency! If I have five dollars, I have either five one-dollar bills or I have some other denominations that happen to add up to five dollars. There is no singular dollar—there are many dollars!
Even if the US dollar were the only dollar in existence, the word dollar still wouldn't uniquely identify a single entity. And the same is true of the word cedi. If I have two cedis, I have two hundred pesewas. There is no singular, unique cedi to which the word refers. So semantically speaking, we have no motivation to treat the word as a proper noun. And syntactically, we don't: I can say a cedi or three cedis, just as I can say a dollar or three Australian dollars.
Ultimately, even if it made sense to treat cedi as a proper noun, the fact is, we don't use it like one, so it isn't one. Any additional explanation is just icing on the cake.