Dansk Her&Nu, also known as Dansk her og nu and Danish Here & Now, is a free online beginner-level Danish course developed with support from the Danish government. The only catch is that it’s all in Danish.
If you’re a complete beginner, you’ll probably struggle without the support of a teacher. Lesson one dives straight in with three relatively long texts, each 7–10 sentences long, and then questions you, in Danish, about whether you believe Danish people greet each other politely or kiss too little.
However, if you’ve already got a little Danish knowledge, or you can work through it with a friend or teacher, it seems like it could be a good supplementary resource. There’s plenty of audio recordings and vocabulary, plus some clear grammar explanations, exercises, and cultural information.