Yes, change at Skanderborg. Be careful of the journey options that involve more than one change but may appear to be quicker. These seem to include a bus for part of the journey whcih may not be your cup of tea. The Danish word for train is 'tog' pronounced a bit like 'toe' in English. The word for 'bus' is 'bus', in case you wondered
I now have my train tickets and seat reservations for the sections Skanderborg to Copenhagen. I bought them as separate tickets, Copenhagen Central to Herning leaving at 10:00 on the 27th and Herning to Copenhagen Airport leaving at 10:08 although these tickets can be used on any trains. I wouldn't expect the seat reservations to be valid on others, of course.