as a non-EEA graduate you don't have the same right to get unemployment benefits as if you were coming from an EEA-country.
BUT you can still (under some conditions) being eligible for unemployment benefits. Please read our article targeted non-EEA graduates and their rights to unemployment benefits.
Also read more: http://a-kasser.dk/graduates/.
You will not being able to get unemployment benefits from day 1 after ending study, because you have not been (free) student member of an A-kasse for at least 1 year. But you can sign up from 6 monts before finish study. Its free membership until you graduate. When you apply (you can do this online) tell the A-kasse that you want status as graduate.
You can get benefits from 1 month after ending study and as long you have residence and working permit (to work full time/37 hours per week). This means for non-EEA graduate normally only in summermonths june, july and august.