Google rolled out the ability to directly search for flights last September, but the first version only covered flights in the US. The latest update now includes international destinations, but still only looks at flights which include America. So you can search for San Francisco-Sydney, but not Sydney-Melbourne.
The searches into Australia only cover capital cities and a handful of larger regional centres. Those limitations means you won't be able to rely on Google Flights as your sole travel research tool, but if you are travelling to the US it can be useful as a means of working out potential costs and routes (albeit with the need to perform multiple searches in most cases, since you always have to start with a US city and thus will need to search twice to get return flight details starting in Australia).
In some instances you're linked directly to a booking page for the relevant airline; other results suggest you have to "contact airline directly". You'd think Google could at least include a link to the airline home page; all that requires is some kind of search engine . . .