I cycled from Rodbyhavn to Copenhagen a couple of years ago on the way from London to Copenhagen and it took us about a day and a half. Don't know if you have any time constraints but we were pretty keen to get to Copenhagen at the end of a long trip and in time to see the worlds that were coincidentally on at the same time. What I remember was that cycling in Denmark is awesome and everything you hear about Copenhagen cycling is true.
One thing you might want to think about is getting across from one island to the next. Our route included stopping at an awesome guesthouse on the island of Bogo (a nice little place called Stalden Bed and Breakfast). We had planned to get the ferry from a little town called Stubbekobing across to Bogo. We knew that the ferry was seasonal but didn't know the exact dates that it ran. We had got the ferry from Cuxhaven to Rodbyhavn earlier in the day and busted a gut getting to Stubbekobing hoping to get the last ferry of the day, only to turn up to the little cafe that doubled up as the ferry stop to find out that the route had closed for the season a few days earlier. Because the only bridge onto the Island was the motorway that bike weren't allowed on, we were faced with a pretty big detour. Thankfully, a call to the b+b owners and they came picked us up. They have a little restaurant attached to the b+b, but it turned out the day we got there was the owners night off, but they made us all a lush dinner, went out themselves and said help yourselves to some beer. So yeah, make sure the ferries are running if you intend to rely on them.
So from Bogo, we crossed over to the Island on Mons and then up the coast to Copenhagen in time to see the end of the womens ITT and then spent about an hour trying to find the little mermaid.
hope this helps, and make sure to down a few pints of tuborg, oh and the carlsberg tastes better there, you can actually drink it.