If you are allowed to work full-time and can take job with one day notice, and you meet the other requirements for being eligible as a graduate, then you can get dagpenge.
Be aware that you must have been in Denmark right before starting your master and again at latest 14 days after graduation.
If you only have a study permit, then you are not allowed to get dagpenge. In a study permit there is included a 6 months jobsearch permit. However this does NOT include right to work, only right to stay in Denmark and look for job. If you get a job you need a new residence- and workperit.
So its important you are fully aware of what kind of residence - and work permit you have.
Anders Weber, www.a-kasser.dk