The professor seems to be right about dinkum originating in England and being associated with hard work. But of course, the word and the expressions fair dinkum are now quintessentially Australian.
The OED notes that the 1900 English Dialect Dictionary records dinkum “hard work” as being in use in English dialect:
1900 Eng. Dial. Dict. II. 80/2 You have gotten to do your dinkum, soä you understand.
However the earliest citation is by Rolf Boldrewood, a pseudonym for English-born, Australian writer Thomas Alexander Browne:
1888 ‘R. Boldrewood’ Robbery under Arms v, It took us an hour’s hard dinkum to get near the peak.
Given that Browne emigrated to Australia when he was five years old, it’s a fair guess that he picked the word up in Australia and didn’t import it from England himself. But he does use it in the dialectal sense, so he’s not far removed from the source.
So it appears to have been an obscure English dialect word that emigrated to Australia, where it flourished.
The ultimate etymology is not known.