Thank you for correcting me ! ^^
A considerable number of ANU Science Phd graduates are teaching in the US, and some of them are department heads in top universities such as UC Berkeley, and Ivies.
Perhaps, it is generally more difficult for people who get their phd from outside North America to get a job offer from American top universities. Nevertheless, as far as I know, many Asian studies academics at not only ANU but also Melbourne and Sydney have taught in US top departments (or institutes like Hoover and Olin) as visiting professors.
For your information, ANU department of politics and department of international relations do produce top graduates. Have you heard of Ian Clark and John Vincent? Ian Clark was the dean of Cambridge's School of Historical and Political Studies (Sorry, I forgot, but he was the dean of Faculty of Social Sciences or something equivalent), while John Vincent was a leading professor at LSE and a core figure of English School. I believe some of the Phd graduates also got postdoctoral fellowship and research fellowship from Top institutes like Oxbridge and IISS.
Anyway, it is pointless to discuss stuffs irrelevant to the current post. It could not be wrong for OP to do his or her phd in the US. However, the US universities may not have dedicated East Asian research institutes, so it may be difficult for him or her to find someone who match his or her research interest. Since Australian universities, particularly ANU, can accommodate most Asia-related topics and provide excellent research training, in my humble opinion OP should not ignore those good universities just because they are not in the US or UK.
Anyway, do many of the Heidelberg, LASEMA-CNRS, Leiden, Rhur graduates teach in top US departments? Many Harvard, UC Berkeley, Georgetown graduates are teaching in Leiden and Heidelberg? Obviously not, but it does not mean they are not good. Reputation is apparently not the only factor that should be and is considered.