Either is grammatically correct, but they carry different meanings.
Using 'the national animal' means that there is only one national animal of Australia.
Using 'a national animal' means that there are several national animals, and the kangaroo is one of them.
Edit: If you can trust Wikipedia, Australia does have two national animals, so 'a national animal' may be the better choice if you're concerned about making your sentence accutate as well as grammatically correct.
Edit #2. I guess though, that one is a national animal, and the other is a national bird. So depending upon how semantically accurate you wish to be, perhaps 'the national animal' is the most accurate choice.
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