if you are citizen from another EU-country (EU National) then you have the right to stay and work in Denmark. You dont need a residence permit.
Registration required after 3 months
However after 3 months in Denmark you are required to register with the relevant authorities (often the City Hall or the local police station) and receive a registration certificate.
Permanent residence permit after 5 years
As an EU citizen, you are automatically entitled to a permanent residence permit in Denmark if you have been legally resident in Denmark for at least 5 consecutive years. If you meet that condition, you can request a permanent residence card, which confirms your right to live permanently in Denmark, without conditions.
If you are interested you can read more about the right to receive permanent residence permit after 5 years, here:
So.. as an EU-citizen there should be no reason for concerns about getting permanent residence.
Receiving Unemployment benefits ("dagpenge") from an A-kasse will have no negative impact for you.
Anders Weber, www.a-kasser.dk