you do not mention which country you are from.
Citizens of the EU/EEA countries, Switzerland or the Nordic countries don't need residence permit and you can get benefits from danish A-kasse if you meet the (other) conditions to be eligible for unemployment benefits. http://a-kasser.dk/benefits.html
If you are NOT from a EU/EEA country then you need to have residence permit in DENMARK
to be eligible to get benefits.
I'm leaving Denmark 8th of February because I got the apartment to live in Iceland. The thing is, that it's necessary to be registered in the job center and also, have applied the PD U2 format least four weeks before departure. I will be graduated 27th of January, after that I will have 10days till my departure. Can I register into the job center now? And also ask to fill up the PD U2 form now? Thank you