you tell you "are from an EU Country". We assume this means you have citizenship from another EU country.
As an EU-citizen this means you can take advantage of the princip of "free movement of labour".
This also applies if you complete an education in Denmark, with a duration of at least 18 months/3 semestre.
As mentioned in our article for graduates this means that you must have permanent address in Denmark before you start education and also at latest 14 days after finish education.
Is has no effect that your deadline has been extended.
If you finish with a thesis that you do not have to defend orally, you can be admitted to the A-kasse the following day after the supervisor and censor (s) have signed a pre-approval.
It seems that you have not been (free) member of an A-kasse as a student. This means that you must accept a quarantine of 1 month before you can get Unemployment benefits.
But you can sign up now with an A-kasse. Up to 6 months before you finish eduaction, the A-kasse can give you the status "graduate" (dimittend in Danish). And membership will be free until your graduation.
What A-kasse should you choose?
"Min A-kasse" has a reputation of having very few complaints from its members. Its also cheap. Two things that we think is important when choosing A-kasse.
On the other hand Min A-kasse do not offer the same offers to its members, in relation to events, networking, meeting employers etc.
So it depends on what you think is important for you.
Both are good choices, and we can recommend both.