If you are a citizen of a Nordic country (Finland, Iceland, Norway or Sweden), you are free to enter, live, study and work in Denmark.
You do not need to apply for neither an EU residence document nor a residence and work permit, since you have the right to reside in Denmark without any permission when you are a citizen of a Nordic country.
You may as well enter Denmark without a passport. However, you must always be able to identify yourself by means of, for example, a driving licence or a payment card.
You can read more about residence in Denmark as a Nordic citizen on newtodenmark.dk:
