As a graduate, there is no certain minimum length of membership in A-kasse required. You can go to Germany after graduation and get the unemployment benefits from the danish A-kasse for 3 months, and then cancel membership. If you get a job before the 3 months period has ended, you can just cancel your membership in the danish A-kasse and get registered in the Germany unemployment Insurance system (see below).
If you stay longer than 3 months in Germany, you will not be allowed to receive unemployment benefits anymore form the danish A-kasse. If you don't return to Denmark before the 3 months period expires, then you can only get unemployment benefits from the danish A-kasse again, after you have worked for at least 296 hours within a period of 12 weeks.
If you find a job in Germany
As a rule, when working in Germany (another EU/EEA country), you must cancel the membership with your danish A-kasse, as you are thus covered by the unemployment system in Germany. It is always the EU-country in where you work, that you must be insured in. And it is only allowed to member of 1 A-kasse at a time.
However be aware not to cancel membership before you are fully aware that you have been included/signed up with the Unemployment Insurance in Germany.
If you move within EU/EEA it is possible to transfer earned rights (working periods, and insurance periods) from/to Denmark. You can read more about this in this article.
Anders Weber, www.a-kasser.dk