you will only be able to apply for/get dagpenge if you have the right to recide and work full time in Denmark. And you must be able to take any kind of job with one day notice.
We do not guide about residence/work permit, but will recommend you to contact SIRI in case you are in doubt whether you have the right to stay and work full time in Denmark.
However as far as we know the family reunification scheme gives you right to stay and work full time in Denmark.
And if you complete an education and meet the requirments for graduates, then you should be able to get dagpenge after the graduate rule. And because you have been member for at least 1 year when graduating, you can get dagpenge from day 1 after graduation. You will not get the 1 month waiting period.
Let me know if you have further questions.
Anders Weber, www.a-kasser.dk