Osaka Kansai Airport to Fukuoka?

I arrive at Kansai airport at about 7pm and need to get to Fukuoka. Since I arrive late evening, I thought it best to stay that night at a airport hotel (cheap) and then leave the next morning to get the Shinkansen to Fukuoka. I see a flight is 24000 yen compared to the Shinkansen at 6000 yen. So the Shinansen wins, and I can also see the countryside on route.
Question, is this a sensible choice?

I see a flight is 24000 yen compared to the Shinkansen at 6000 yen.

I am afraid you got wrong information. The correct information is here:
http://www.japan-guide.com/e/e4802.html?aFROM=2157_2161

To summarize: if you do not mind flying the discount airline Peach, you can fly from Kansai Airport to Fukuoka for as little as 3500 yen (more expensive on busy days), but luggage costs additionally. The shinkansen costs 14,000 yen one way fro Osaka to Fukuoka, plus another 1000-2000 yen to get from the airport to Shin-Osaka Station.

So, if cost is the highest priority, air is likely the better option. If money is secondary, I would select the train, though, because I find trains more comfortable than airplanes. Time wise, the plane wins over the train.