An alligator is indeed a specific thing, but not capitalized because it could mean any old alligator. The species name is gnerally capitalized athough this may be old-fahsioned as I'm seeing species names uncapitalized now fairly often in professional media.That doesn't make it a proper noun, it just makes it a noun. And alligator is a specific thing with a specific name, too. But you don't capitalize it.
Australian is a proper noun. A proper noun generally refers to a distinct thing, with a name that is generally attached to it's individuality.
Australia (proper noun) is a name for a country (noun, not proper).
In German all nouns are capitalized. In English they are not, only proper nouns are. All proper nouns are nouns, but not all nouns are proper.
We seem to disagree over what is a proper noun (not captialized, oddly enough). Language is a funny thing and the rules tend to come from very irregular, random-seeming... after all it arises from the behavior of people as they speak or write, and who is less consistent and rational than people?
But specific things like Australia, Charley The Alligator, the Etchells 22 Class, etc etc, are proper to capitalize. RandOm nouNs, not so mUch.