If you ever find yourself at Suvarnabhumhi and suddenly realise that your flight leaves from Don Mueang across town then don’t panic. As long as you arrived in good time you should get there on time.
I just made this same mistake and had to do a mad rush across town. I was very lucky that the traffic on the tollways wasn’t that bad. It only took 33 minutes but you should really allow for one hour.
For the record, the taxi fare was 315 Baht and the three tollways fees came to 130 Baht.