my answer do not take into account problems with entering Denmark related to Corona. You must address corona-related questions to others. Without knowing it for sure I think you can enter Denmarks border if you are registered as a student in Denmark.
If you are allowed to enter Denmark, then you must be here at latest 2 weeks after graduation in order to be able to get graduate rights in the A-kasse. You do not need to stay here the full 2-week period - the rule says that you must be here and get registered as graduate in A-kasse, at latest 2 weeks after graduation.
Off course you can only get dagpenge, if you are available for the danish labor-market. So you have to come here anyway. However you can have dagpenge from a danish A-kasse for up to 3 months while searching for job in another EU-country.
Generally about EU residence:
You do not need an EU residence document in order to begin work. And therefore you can also apply for Unemployment benefits ("dagpenge"), if you meet the conditions for rights to dagpenge as a graduate.
In Denmark, you will, however, in many situations need a Civil Registration System (CPR) number. You must present your EU residence document to your municipality of residence to be given a CPR number (and health insurance card and the like).
If you plan on remaining in Denmark for less than three months, you do not need to apply for an EU residence document. If you are seeking employment, you may remain in Denmark for up to six months before obtaining a residence document.
If you plan on being in Denmark for longer than three months, or six months if you will be seeking employment, you need to apply for an EU residence document. If you have a residence document, you may remain in Denmark indefinitely, provided you meet the conditions for your grounds for residence. There is no date of expiry for residence documents.
If your grounds for residence are terminated – e.g. if you stop working or studying – you must apply for a new residence document on other grounds – e.g. as a person with sufficient funds. If you are uncertain whether you meet the conditions for new grounds for residence, you must contact SIRI.
Read more about residence as an EU/EEA citizen at SIRI homepage.
Anders Weber, www.a-kasser.dk