it is quite simple for you (EU-citizen) to receive dagpenge after graduation.
I assume that you have stayed in Denmark before the start of the education. And You will stay in Denmark after graduation you tell.
Also I assume that your education has a duration of at least 18 months/3 semesters.
Finally I assume that you meet the residence requirement.
You have been member for more than 1 year...this means you can get benefits from day 1 after graduation. You will not have 1 month of quarantine.
To receive benefits AS AN GRADUATE you must contact your A-kasse at latest 2 weeks after graduation and tell them that you now have graduated, and you want
to be registered in the A-kasse, with graduate rights/status.
Normally you can contact the A-kasse up to 3 months before graduation and be registered with the graduate status. However this differs among the A-kasser, how early you can do this.
Try maybe to contact your A-kasse to ask if its possible now, or just remember to do it at LATEST 2 WEEKS AFTER GRADUATION.
You tell also that you have been working. But you don't tell how much. If you have had an income for at least DKK 233,376 (in 2019) during the last 3 years (in total), it may be possible to have unemployment benefits as an wage-earner (insted of graduate). Remember that only income earned during periods where you have been A-kasse member can be included to meet the income-requirement.
This means a higher benefit rate. But for being a better solution for you, it depends on different things - this will be too much to explain here. But if you think benefits as a wage-earner would be an option for you, try to ask your A-kasse about that.
Anders Weber, www.a-kasser.dk