your rights to get unemployment benefits is only depending of you have completed education of at least duration of 18 months (3 semester).
"Breaks" dosen't matter as long you graduate.
As new graduate you are quaranteed to get benefits after the special rule for graduates (benefits from one month after graduation).
If you have been member of an A-kasse for at least one year before graduation you get benefits from day 1.
If you get salary over 215.020 DKK from your internship you are not eligible for free membership of an A-kasse.
Otherwise just be sure to become member of an A-kasse at least one year before ending master-study if you want benefits from day 1.