Flight Haneda Airport departs from Tokyo Haneda Airport at 18:40 and arrives at Fukuoka Fukuoka Airport at 20:40.
The flighttime is about 2h 00m. The distance travelled ("as the bird flies"): 1048 Km. So the average speed is roughly 524 Km.
The best day to arrive at Tokyo is Thursday and it would be best to avoid Monday, as prices are on average 176.32% higher than on Thursday. (Average prices, based on 3134615 datapoints.)
We have a lot more statistics for flights JL 331 and between Tokyo and Fukuoka.