because you are an EU-citizen then you have the right to stay and work in Denmark without the need for a specific work-permit.
This is one of the requirements for being eligible for Unemployment benefits...that you can work full time.
The other requirements are that you must have been member of an A-kasse for 1 year, and that you within the last 3 years in total have earned at least DKK 228,348 before tax (in 2018).
You can see the general requirements here: https://www.a-kasser.dk/benefits.html
For being able to receive Unemployment benefits you must off course stay in Denmark when you apply for the benefits, and in the period you receive benefits.
However you have the option to transfer Unemployment benefits to another EU-country while looking for job there. It can be done for a period of up to 3 months. read more about this option here:
If you plan to move to another EU/EEA country after being in Denmark, then the periods with insurance and working can be transfered to the other EU-country. So if this is the case for you, it will be a good idea to become member of an danish A-kasse, also if you only stay here for 1 and a half year.
You can read more about principles of transfering periods with insurance and work to Unemployment Scheme in another EU-country, however our article is covering the case where people move to Denmark from another EU-country. https://www.a-kasser.dk/transfering-periods-of-work-and-insurance-from-another-eea-country.html
Hope this helps you, otherwise you are welcome to comment here.