Dear Arwa, "Fair dinkum" does mean "true", "the truth", "speaking the true" or "agree" :) Nowadays no one uses this expression in speech, it is considered to be Australian, but was derived most probably from East Midlands of England where it meant "hard work" or "fair work". The phrase today is vastly used in jokes. Hope, it helps :)

"Fair dinkum" is Australian slang. It means "true", "authentic", "genuine", "honest", "fair/just". Australia is a fair dinkum country where social justice prevails, and everybody has a fair dinkum opportunity to enjoy a good life.