if your education meets the requirements (at least 18 months duration, and SU-eligible), then you are entitled to get dagpenge after the "graduate-rule", if you sign up for A-kasse at LATEST 2 weeks after graduation.
It would have been advantage if you already was student member in A-kasse now, and have been member for at least 1 year when you graduate. In this way you would have avoided the 1 months quarantine, that you will get.
If you have decided NOT to continue your part-time job after graduation, then it is best to stop the job before graduation, because then you will not get the normal 3 weeks quarantine for self-inflicted unemployment.
If you want to continue your part time job, it could be an option for you to go on "supplementary unemployment benefits ("supplerende dagpenge"). In that case, you may find some useful information in our q&a's tagget "suplementary benefits".
After graduation, and when you have recievd dagpenge for 4 weeks you can go to another EU-country to search for job, and at the same time keep your dagpenge from the danish A-kasse for up to 3 months. You can read more about that option here:
Let me know if you have further questions.
Anders Weber, www.a-kasser.dk