Yes you can get unemployment benefits ("dagpenge") also when you decide to leave job your self, i.e. not get fired.
However when you quit job your self you must accept an quarantine for 3 weeks, where you will not receive dagpenge.
So, from the date you stop work, there will be a period of 3 weeks before you will begin to collect dagpenge.
There are some few valid reasons for quitting a job, that dont result in the 3-weeks quarantine, but this does not include that "you don't like the job". We have answered another question about valid reasons that will not result in quarantine. You can find the Q&A here: See Q&A about valid reason for avoiding quarantine with dagpenge
You dont tell how long you have been in your current job, but as an recent graduate it is possible to get your dagpenge amount (in danish: "dagpengesats") recalculated after 6 months from graduating, if you have had worked at least 320 hours in the period from graduation and until you apply for dagpenge (again).
If you at the time have had a monthly salary (before tax) for at least DKK 22,503, then it will possible for you to get the highest possible amount in dagpenge, which is DKK 18,633 per month.
If you have worked at least 320 hours in your current job, you should ask the A-kasse to have your dagpenge amount recalculated. If you at the moment is close to have worked 320 hours, then you should consider to wait quitting job before you have reached the 320 hours of work.
If you dont meet the requirements for getting your amount recalculated, then you will continue receiving the same amount that you received as an graduate, before you started in the job. If you don't have dependent children this will be only 71,5% of the DKK 18,633 or DKK 13,323.
Hope this helps claify things for you. You are welcome to comment on this page.