20,M Australia --> Denmark (or Sweden)

I'm in my 2nd year in an Arts bachelor focusing on politics subjects and really want to move to Denmark at least for a while after I'm done. Obviously my degree won't help me out in getting any sort of specific job, so is there any sort of other job that I could come over and do and be allowed to stay? I speak about B2 Swedish and am pretty familiar with Danish so think I could get it up to a pretty good level relatively quickly were I over there. I also love the language so would want to do this anyway. I would love to study there after my degree but without EU citizenship this would probably be a bit too expensive...