I agree with Andrew. Get a local card ASAP if your spending money on a AUS CC. With the International fee + the hassle of trying to pay every month, without an Australian income , creates more problems and head aches.
As an Aussie in the US as well, the only way we could get a US CC in the first 1-2 years was to get a secured Visa card. Meaning you have the money in the bank, and they allow you to use the card up to the limit to whats in the account. Bit silly, but this allows you to get a credit history, then unsecured cards become available. Not sure how credit works in Denmark, but im sure they would offer something similar.
Rob