Hi
the permission you have to stay in Denmark is a student permission and after finishing your study you have additional 6 months job search permission. This also give you right to work 20 hours per week. But in summerperiod (june, july and august) you can work full-time.
You are entitled to getting unemployment benefits (dagpenge) as an graduate only for the months where your studypermit (which includes a limited working-permit) gives you right to work full-time (june,july and august) and also you should be available for taking job with one workday notice.
You can read more in our special article targeted non-EEA graduates and their rights to unemployment benefits.
According to your information it seems that you have not been free studentmember of an A-kasse for at least 1 year before ending study. Because of this you can not get benefits from day 1 after ending study. You will get one month quarantine before you can start receive benefits.
But you should be aware that since 1. of january 2015 it has become less attractive for internastional(non-eu) students to receive dagpenge as an graduate. If you as non-eu graduate gets benefits (dagpenge) you can NOT at the same time get greencard or establishment card. So if you apply for grencard or establishment and get it, it will be with condition that you stop receiving unemployment benefits.
Best regards
A-kasser.dk