What are good children's books written in Danish?
Here is a website that has some Danish picture books that you can access online: http://www.childrensbooksforever.com/childrenpages/Danish.html
Another great website for children's books around the world (including Denmark) is The International Children's Digital Library. This has a number of books you can read online, and will also give you the names of some popular Danish children's book authors that you can then look up in WorldCat and possibly request via interlibrary loan.
The Danish Literary Magazine devoted an issue this year to children's and young adult literature that could also give you some titles to search for.
Amazon has a list of children's books in Danish, although many of those seem to be Danish translations of English-language children's books.
I hope this gives you some places to start! And do feel free to suggest for purchase any good Danish titles you find.