To clarify a few things.
Westcoast of Jutland is flat, then gets more hilly as you move East, this is all down to where the glaciers where during the ice ages.
The islands have got their hilly parts compared to the West but ofcourse its not really much of hills if you are from the UK.
There is only 1 place in all of Denmark with rock (Northern Jutland is all sand, Europes largest moving sand dune is there),the island of Bornholm where they actually have a downhill track (again not much if you are from the UK)
There is many tracks made lately in the flat western parts which is sandy soil with pine/fir woods
As Ebygomm says the area around the lakes at Silkeborg is the hilliest place you will find for riding.
North Sjælland got lots of nice riding around the woods
You can do a great bike packing trip up the West Coast of Jutland following North Sea cycle route
https://www.flickr.com/photos/83246699@N00/albums/72157622347428986
you cant wild camp in Denmark but there is a lot of shelters build for overnight stays you just need to know where to find them.
I grew up on the flat west coast and used to find it a bit boring, now after living in UK for 12 years i have really got to appreciate the flat open space whenever i get back home.