you can register for a-kasse as long as you still living in Denmark.Are you moving to Sweden you have to be member of an swedish A-kasse. You can only be member in one country.
Will you be eligible for unemployment benefits as a graduate?
For being eligible for unemployment benefits you must meet the requirements for graduates. Read more here: http://a-kasser.dk/graduates/.
One of the requirements is that you have to participate and finish an education of duration for at least 18 months (=3 semestre). Be aware that - as the rules are now* - it is the program's actual duration, which is crucial. So, if you begin study - for example- in mid-January and goes up to the final exam at the end of June, next year, then you education only have a duration of 17 months.
*New rules from January 2, 2017
As part of the new unemployment insurance system, which comes into force January 2, 2017, the rules governing the program's actual duration probably will be changed. We expect that the new rules gives you the right to unemployment benefits, if the program is rated to 18 months. However not from earlier than 18 months after you started the education.
The law has yet to be approved.
Another requirement is that you have to stay in Denmark latest the day before starting your education and also latest 14 days after ending study.
About the education/study:
It is NOT a requirement that the study must be carried out in Denmark. Also it is NOT a requirement that the education is offered by a Danish school/University.
But to give right to unemployment benfits the education has to meet the same criteria as a Danish education qualifing for graduates benefits, including requirements for SU-justification.
You must ask your A-kasse if the education you plan to study in Sweden meets the criteria to be compared with a danish SU-justified education.
Read more about SU here: http://www.su.dk/
About what A-kasse to be member of?
A high education at university in "service and service management" is covered by "MA A-kasse". So we will advice you to be member of "MA A-kasse".