Hi,
if you complete the master and graduate as expected, then you will be able to get unemployment benefits after the graduate rule. So the fact that you NOT have been (free student) member or paid part-time member for at least 1 year when graduating, only means that you have to wait one month before you can begin to receive unemployment benefits (dagpenge).
You will get 1 month waiting-period, because you have not been member 1 year before graduating, and It’s not possible to avoid this 1 month waiting-period. The A-kasse can not make any exceptions.
Best regards,
Anders Weber, A-kasser.dk