I am an Australian citizen and studying at University of Newcastle (Australia). Does your graduate school reputation has any effect in your academic career? So if I decide to do my PhD at a US university (like Harvard or Stanford) instead of doing it at an Australian university (say University of Melbourne or Australian National University), would that make me more successful in my academic career? Does that make me more employable? Say that after doing my PhD, I apply for an academic position at a Canadian university, which of them would help here more?
The short answer is yes, of course.
The long answer is, it depends. Ultimately, your future career will depend on your publications and other output, their quality and their impact. If you can produce a number of high quality publications from a lower-ranked university, this will be better than producing nothing of interest from a higher-ranked university. However, the chances of "succeeding" are higher at higher-ranked universities, because they have "better" people to help you along the way. They also have higher standards and more pressure. So there will be a bit of a trade-off.
That said, the University of Melbourne and ANU are good places.