I think that Italians would rather move to another Romance-language Catholic country than a Germanic-language Protestant one. Many settlers in French Algeria were Italian, and millions of Italians emigrated from Italy to Brazil and Argentina. I also think that Greeks and Arab Christians would head to French Australia.
In Dutch Australia I could see a large German and Scandinavian population (Germanic-language Protestants, although Southern Germans are Catholics).
That is true, if the immigration is early enough (when Italy was regional) i think it could be very easy. Arab Christians i could see. Greeks is possible too I guess.
edit: also noticed Vietnam (or that area) is French. I could certainly see a lot of immigration from there