The distance is less, but taxis in Copenhagen are expensive - expect to pay Kr250-300 (around the US$40 mark). But they are reliable and straight up. I'm sure the hotel can arrange one, but otherwise Taxa and Dantaxi are the big ones.

If you don't have a load of luggage, there are trains from the main station (opposite the Royal) which take 17 minutes to the airport. However, due to the border nonsense going on with Sweden, this is currently only every 20 minutes.