as long as you still receive salary, then you are regarded as still employed (not unemployed) in the unemployment Insurance system.
So you can take it easy. But on the first real unemployment day (in 3 months) you must register as unemployed at your local Jobcenter or at Jobnet.dk.
The same day you can apply for unemployment benefits ("dagpenge") in your A-kasse.
I assume you meet the requirements for being eligible for dagpenge. You can have a look at them here.