I can't see any trains at 1309 for upcoming Fridays. What date is this for?
Are you flying into MUC? If not I would rather take a train all the way from Munich - and personally I don't think first class is worth it for a 1.5 hour journey (while it might be for a 6.5 hour journey) especially when the 9 euro ticket is available and an ICE only saves about 10 minutes over a direct RE, which is also pretty comfortable.
(I travelled from Duesseldorf Hbf to Bielefeld myself on RE trains last week.)