I hate to be picky, but ".. .. .. was born in Capital Territory, Australia." just looks weird and totally wrong.
It should be (with or without the "the") "Australian Capital Territory" (I don't honestly think it needs another Australia to follow). It's not "Capital Territory, Australia". The official name is not "Capital Territory". (The Australian Capital Territory was known as the Federal Capital Territory until 1938.)
I don't know that I've ever seen the/The Northern Territory, without a "the" i.e. The Northern Territory (officially the Northern Territory of Australia) .. but I could live with it without a "the" if that's too picky even for picky.
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(Isn't tweaking things fun?! )