The train connection between Düsseldorf Airport and Cologne Airport is quite good, however the commuter trains could be very crowded during rush hour, so you might think about a first class ticket.
Some ICE and IC trains are stopping at Düsseldorf Long Distance railway station (do not mix it up with the S-Bahn Station in the Terminal). The train station is connected with the terminal by the skytrain.

Travel time between DUS and CGN is app. 35 – 40 minutes, depending on the train you choose.