Copenhagen to Germany

There is a night train.
We are taking a night train from Copenhagen to Cologne, Germany in just a week.

Copenhagen to Hamburg is 4 1/2 hours by train that crosses on a ferry between Rodby and Putgarden, runs during the day. Same train would bw another 21/2 hours or so to Berlin.
We are taking this northbound during the day next month specifically so we can enjoy the trip.

There are also ferries (walk-on) from Gedser, Denmark, to Rostock, Germany, or also departing from Malmo, Sweden, to Germany; see www.aferry.com. See also How to Look Up Train Schedules Online for the DB train schedule link and tips for using it.

My first question is where in Germany, getting to the border is one thing but are you planning Kiel, Rostock, Berlin, Hamburg, Koln, Frankfurt, Munich or somewhere else?

If it's Kiel or Rostock, I'd seriously consider a ferry. Trains and ferries are really expensive so be ready for sticker shock. I looked at a train from Copenhagen to Hamburg and the train was put on a ferry for part of the trip. The primary purpose was a short visit to see my wife's cousin, because of the price and her cousin not having any vacation time left, we decided against it.

Anywhere else, I'd go with a short hop on a low cost European Airline. It will be both more convenient and cheaper.