As already stated, your best bet is probably taking a taxi straight between the airports.
A very useful tip (besides making sure you have Thai baht currency) is to head straight for the elevator in DMK when you arrive, clear immigration and have your luggage. Take the elevator up to the departure level, head towards the entrance/exit and wait for a taxi to come and drop someone off. Most taxis will gladly pick you up instead of having to wait at the arrivals taxi queue!
I have done this two times and it has been very successful - the second time there was literally zero waiting time, I was in a taxi heading to my destination within 5 minutes of grabbing my luggage!
The other time I made the mistake of first heading to the taxi queue, getting a ticket and eating a quick meal while waiting... I gave up after 40 minutes when I realized it would take me at least an hour more, and headed to the departure level entrance where I waited about 2 minutes (there was one other couple who was also waiting for a taxi).
Even so, it will probably be super tight, so you just have to hope for the best regarding delays, luggage, traffic, etc. Make sure to tell the taxi driver to take the tollway/expressway. A useful phrase in Thai might be "leo leo", meaning "hurry" :D
Another option would be to check with the airline you're going with to Samui (I'm guessing Bangkok Airways?) if it is at all possible to reschedule the flight?