Hi,
when you are allowed to work full time in Denmark, and can accept any job with one day notice, then you have the same rights as danish citizens in relation to A-kasse/dagpenge.
If you complete a public recognised education with a duration of at least 18 months, then you can get dagpenge according to the special graduate-rule. Remember you must apply at latest 14 days after finishing the education.
As mentioned your education must be public recognised, meaning that the education must be SU eligible.
If you have more than 1 year until graduation you could benefit from becoming member in A-kasse now. With at least 1 year membership at graduation, you can avoid the normal 1 month waiting period with dagpenge.
Because you are over 30 years old, you do not qualify for free membership. However, if you have more than 1 year left, I will recommend that you sign up for A-kasse.
You should probably become member in Akademikernes A-kasse or MA A-kasse. You can find links on our site, www.a-kasser.dk to the A-kasse websites. You can sign up online, or call them to become member.
Best regards,
Anders Weber, www.a-kasser.dk