Not sure how everyone feels about China Eastern, and I can't comment as I haven't flown them myself, but those prices! Can't say they're not bargains. With some dates in summer (August), too.
These are via Shanghai, and some of the stops are long but you have options: China Eastern offers free transit accom if you have a stop over 6 hours and meet the criteria, otherwise, most are daytime stops so also possible to go spend a day in Shanghai (you don't need a visa for short stays).
Melbourne to Venice $1072
Melbourne to Rome $1093
Melbourne to Budapest $1096
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Wow so cheap, any real experience from people here