thank you for your question.
One of the important requirements for being able to receive dagpenge is that you have right to stay and WORK FULL-TIME in Denmark.
A student visa for international (non EU) students only gives you limited right to WORK in Denmark. You have the right to work up to 20 hours per week. However in the summer months june, july and august you are allowed to work fulltime.
This maximum of 20 hours per week also applies in the 6 months job search period after completion of education, included with a student-visa.
In other words - A study visa is not compatible with receiving dagpenge.
If you get a new VISA which gives you right to work full-time in Denmark then you will be eligible for getting dagpenge after 1 year membership of an A-kasse, and 1 year of work/income. We have a specific article on our website, that explains in details conditions for entitlement to dagpenge.
So before you are sure that you can have a working permit/visa it is of no relevance to become member of an A-kasse.
However, as a foreign national who has completed a Danish Matser or PhD degree you can apply for a residence permit with the aim of establishing yourself in Denmark (an establishment card). If you have received a residence permit under the establishment card scheme, you can legally stay in Denmark and can accept offers of employment with one day's notice.
Therefore, it will be relevant for establishment cardholders to apply for membership of an a-kasse.
If you get a VISA only to a specific job-contract (The Pay Limit scheme), then you should also be aware that it is only relevant for you to join A-kasse if you are sure you can stay and work in Denmark after the job-contract ends. If VISA is only for a specific job, you are NOT allowed to stay in Denmark after the job ends, and therefor you will not be able to receive dagpenge.
You can always become member of an A-kasse, but as you can see, you must consider if it will be worth for you to pay membership-fee. This is only a good deal for you if you are sure that you can receive benefits in case of unemployment.
Let us know if you need further help.