thank you for your question.
First, I assume you not have a FREE study-membership of an A-kasse.
If thats right you have to use the rule for graduates. http://a-kasser.dk/graduates/
1. You must be in Denmark no later than 14 days (including weekends) after you end your education.
But remember that you can apply for membership (as graduate) up to 6 months before ending study.
It will be FREE of cost as long you study.
If you do that you will have fulfilled the 2-week rule, but in that case contact your a-kasse when you have graduated
and tell them that you are now graduated and want to have the benefits as a new graduate.
2. Travel when member of an A-kasse?
As long as you receive unemployment benefits from your A-kasse, you must be ready to take a job anytime.
That said, you have the rights as unemployed to have holliday like everyone else.
So off course you can travel, but only normal holiday.
Also if you are an EU-citizen you have more rights to travel to other EU-countries to look for job and in some cases
continue to receive your unemployment benefits from Denmark.
Please ask you A-kasse about the exact rules.