as a start of point you can not get dagpenge, if you have your own business.
If you already have your own business when you apply for dagpenge, then you can only get "supplementary benefits" if your business can be considered as your "secondary" employment. For this to be possible you must have registered at least 80 workinghours in average as wage-earner in the last 6 month before applying for dagpenge.
If you wait to start up your own business until after you have started to receive dagpenge, then you can get supplementary benefits if just the A-kasse decide that its possible to perform your own business and at the same time being available full-time for the labor-market.
To be able to be approved for supplementary benefits you must meet the normal requirements for being eligible for dagpenge. Read more here about the requirements.
It is possible to get supplementary benefits for up to 30 weeks.
Please note, that supplementary benefits is only an option if you can quit your part-time freelance business with one day notice. This means for example, that you cannot enter into contracts that bind you to work at certain times during the day. And like others who receive benefits you must be willing to take a full-time job. You must search for full-time jobs, and you must attend to all meetings in the Jobcenter and A-kasse.
If you quit your job yourself, then you will get the 3-weeks quarantine.
Anders Weber, www.a-kasser.dk