Does the time difference between Melbourne and Sydney change during the year?

No. Both cities keep the same local time all year.

When is the best time to call Sydney from Melbourne?

Between 09:00 and 17:00 in Melbourne, which is 09:00 to 17:00 in Sydney.

Melbourne and Sydney are on the same local time. This gap is the same all year — neither city shifts its clocks relative to the other.

Melbourne

Australia

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Sydney

Australia

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A 9-to-5 day in each city overlaps for 8h. That is 09:00–17:00 in Melbourne, which is 09:00–17:00 in Sydney.

City	Time zone	UTC offset
Melbourne · Australia	Australia/Melbourne	UTC+10
Sydney · Australia	Australia/Sydney	UTC+10

What is the time difference between Melbourne and Sydney?: Melbourne and Sydney are on the same local time. This gap is the same all year — neither city shifts its clocks relative to the other.
Does the time difference between Melbourne and Sydney change during the year?: No. Both cities keep the same local time all year.
When is the best time to call Sydney from Melbourne?: Between 09:00 and 17:00 in Melbourne, which is 09:00 to 17:00 in Sydney.