In order to be eligible for Unemployment benefits after the graduate rule, you must have lived in Denmark no later than the day before you commenced the study, and again at latest 2 weeks after finishing the study.
And the study must have a duration of at least 18 months/3 semestre.
There is no requirement about where/in which country you are living during the study.
And it is also ok, that you take part of your education on another University in another country, as long as it can be seen as a complete education of at least 18 months.
Because you also are an EU citizen, then there will be no problem with residence and work permit, since you have this automatically as an EU-citizen.
So therefore you meet all requirements for being eligible for benefits, IF you move to Denmark at latest 2 weeks after finishing study, and also sign up for A-kasse membership at latest 2 weeks after graduation.
Let us know if you need more information.
Anders Weber, www.a-kasser.dk