As a few people probably know, there will be a partial solar eclipse next week, on 11 September, starting at 10:25 UTC (20:25 Melbourne time). It won't, however, be visible from Australia; in fact, only people in South America (in locations at least 5 degrees south of the equator) and western Antarctica will see anything special. The UK's Nautical Almanac Office has a great map and animation showing the path of the eclipse.
Eastern Australia will see some solar action next year, with a very small partial eclipse in mid-afternoon on 7 February (less than 10% of the Sun will be obscured). That will be part of an annular eclipse (a total eclipse in which the apparent size of the Moon is not large enough to cover the whole disk of the Sun, leaving a bright ring around the Moon), but the path of "annularity" touches only Antarctica and the South Pacific.
For the record, the next total eclipse visible from eastern Australia will be in July of 2028, and it will not be total for Melbourne (it will be for Sydney, though).