ANU is the only place to pursue such a career path. It is one of few universities to teach International Relations and is certainly the premier among those that do.
Bear in mind though that half the campuss also wants to get into the diplomatic corps, and they only accept one or two applicants per year. Needless to say it is very competitive. Check out DFATs profiles of previously successful applicants. Probably a bad idea to pin all your hopes on it.
If you want it though then arts/asian studies, arts/economics or arts/law is the way to go.
In any case in Arts major in International Relations and one of the following: American Studies, Anthropology, Applied Linguistics, Contemporary Europe, Developement Studies, History, International Communication, Linguistics, Population Studies, Sociology, or a Language (Italian, German, French, Spanish, Arabic or Persian).
Economics: Economics and Economic Development.
Law: Admin Law and International Law.
I stress though that an appropriate degree (even with shit-hot marks) is unlikely to be enough (honours would probably e a good idea). They look for experience internationally with either business or NGOs, probably some time on exchange, well rounded character the whole lot.
Other avenues to consider are AusAid (administrators of all our overseas Aid), ASIO (strategic analysis/spies), ONA (analysts), Dep of the PM, or NGO work.