if/when you get registered in the A-kasse with graduate status, then you have up to to years to start using your graduate rights.
As long as you dont use your rights to receive benefits (beacuse you will have vacation), then you should not register as unemployed. You are not eligible for receiving Dagpenge, in the period where you have vacation.
So if you plan to have vacation right after your graduation, then you only need to tell the A-kasse that you want to have your graduate status registered. You do this when you apply for membership (at latest 2 weeks after graduation).
When you come back to Denmark, and if you are unemployed at that point, then you register yourself as unemployed on Jobnet.dk (or your local JobCenter), and also apply for Unemployment benefits ("Dagpenge") in your A-kasse.
Then you can begin to receive Dagpenge, based on your previous registered graduate status.
If you - instead of having vacation/holiday - plan to go to another EU/EEA country to look for job, then it will be possible to have your Unemployment benefits ("Dagpenge") paid for up to 3 months, even if you are in the other country. You can read more about this possibility here: