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

Yes. Because of daylight saving time the gap moves between +1h and +2h.

When is the best time to call Seoul from Melbourne?

Between 10:00 and 17:00 in Melbourne, which is 09:00 to 16:00 in Seoul.

Melbourne is 1h ahead of Seoul. This gap is not fixed: daylight saving time moves it between +1h and +2h during the year.

Melbourne

Australia

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Seoul

South Korea

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A 9-to-5 day in each city overlaps for 7h. That is 10:00–17:00 in Melbourne, which is 09:00–16:00 in Seoul.

City	Time zone	UTC offset
Melbourne · Australia	Australia/Melbourne	UTC+10
Seoul · South Korea	Asia/Seoul	UTC+9

What is the time difference between Melbourne and Seoul?: Melbourne is 1h ahead of Seoul. This gap is not fixed: daylight saving time moves it between +1h and +2h during the year.
Does the time difference between Melbourne and Seoul change during the year?: Yes. Because of daylight saving time the gap moves between +1h and +2h.
When is the best time to call Seoul from Melbourne?: Between 10:00 and 17:00 in Melbourne, which is 09:00 to 16:00 in Seoul.