Flight Haneda Airport departs from Tokyo Haneda Airport at 06:25 and arrives at Fukuoka Fukuoka Airport at 08:20.
The flighttime is about 1h 55m. The distance travelled ("as the bird flies"): 1048 Km. So the average speed is roughly 547 Km.
The best day to arrive at Tokyo is Monday and it would be best to avoid Wednesday, as prices are on average 207.99% higher than on Monday. (Average prices, based on 3134749 datapoints.)
We have a lot more statistics for flights JL 303 and between Tokyo and Fukuoka.