"Doktor" in Denmark is an university degree. You can be a doctor of old latin, doctor of law and doctor of medicine etc. If I'm really ill, I'll prefer the latter, and I will call for a "læge"! (En læge, lægen, flere læger, alle lægerne).
"En læge " usually is not a doctor, but a medical candidate from university. (To be a doctor you have to write (and defend) a long, scientific article based on your own genuine studies.)