as you describe you need to fill out the formular (PD U1). You find information in english about the document here:
If you were a member of a Danish unemployment insurance fund (A-kasse) while you worked in Denmark, please forward the application form (PD U1) to your unemployment insurance fund. If you were not a member of a Danish unemployment insurance fund, please send your application form to the Danish Agency for Labour Market and Recruitment (in danish: Styrelsen for Arbejdsmarked og Rekruttering, website: www.star.dk.)
The form can be completed on screen, then printed and posted. Alternatively, the form can be completed on screen and sent by e-mail as a file attachment.
You can instead ask your previous employer to submit the required information on virk.dk or to complete application form EØS 7.
If you are/were not a member of a Danish unemployment fund (a-kasse), and you wish to know if you are entitled to document PD U1, please contact the Danish Agency for Labour Market and Recruitment.