At least you'll be missing the worst of our weather (June/July).
Melbourne in famous for its changeable four seasons-in-one day weather, and the inability of the weather bureau to predict it accurately.
August - Coldish, maximum typically 17 or 18 Celsius, but can creep up to 22 to 24 sometimes.
September - One nice week 20 - 25 Celsius, followed by three nasty weeks of wet, changeable weather (unless it's a drought year) and there can be a few 30 degree days.
October - Usually warming up (low to mid 20s) in the beginning, a few hot 30 to 33 degree days towards the end. Lots of showers in between.
November - 25 to 30 degree days, coupled with changeageable 20 degree days.
December - usually starts getting hot. Lots of 30 degree or more days, although some cold years it just hangs around 22 for most of the month.
January/ February - usually hot and getting hotter. We had two 43 degree days last year. Unlike other parts of the country, there is sometimes a pattern - 21 degrees, 23 to 27 over a couple of days, then 30 to 35 for a couple of days, then a thunderstorm, cool change, and back to 21 degrees. But some summers are more moderate, some are more extreme.
March - this year it was warm high 20s, sunny weather for most of March. Other years it can turn cold and wet fairly quickly in March, and beach weather ends abruptly.
April - starting to cool down, unless it gets warm.
You can bring your favourite allergy pills if you want, but you don't have to, as our chemists are stocked to the hilt with over the counter hayfever pills and sprays. Our north winds bring the hot weather, and a stack of pollen which leaves many people sneezing and teary eyed.
Hope you enjoy your stay in the city that regularly is scored among the first or second most liveable city in the world.