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

Yes. Because of daylight saving time the gap moves between +2h and +3h.

When is the best time to call Singapore from Melbourne?

Between 11:00 and 17:00 in Melbourne, which is 09:00 to 15:00 in Singapore.

Melbourne is 2h ahead of Singapore. This gap is not fixed: daylight saving time moves it between +2h and +3h during the year.

Melbourne

Australia

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Singapore

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A 9-to-5 day in each city overlaps for 6h. That is 11:00–17:00 in Melbourne, which is 09:00–15:00 in Singapore.

City	Time zone	UTC offset
Melbourne · Australia	Australia/Melbourne	UTC+10
Singapore · Singapore	Asia/Singapore	UTC+8

What is the time difference between Melbourne and Singapore?: Melbourne is 2h ahead of Singapore. This gap is not fixed: daylight saving time moves it between +2h and +3h during the year.
Does the time difference between Melbourne and Singapore change during the year?: Yes. Because of daylight saving time the gap moves between +2h and +3h.
When is the best time to call Singapore from Melbourne?: Between 11:00 and 17:00 in Melbourne, which is 09:00 to 15:00 in Singapore.