You must hold a residence permit in order to function as an au pair with a host family in Denmark, if you are a citizen of a country outside the EU/EEA.
It is your own responsibility to obtain a residence permit.
The purpose of an au pair stay
The term au pair means 'on equal terms'. The idea of an au pair stay is for a young person to stay with a host family with children under the age of 18 'on equal terms' with the other members of the family. The purpose is for the au pair to improve language and/or professional skills as well as broaden his/her cultural horizon by becoming more acquainted with Denmark. In return, the au pair participates in the host family's domestic chores (e.g. cleaning, washing clothes, cooking, babysitting) for a minimum of three and a maximum of five hours a day, and no more than six days a week.
Please visit Denmark Immigration Service website for Au Pair and Intern information.