Flight Haneda Airport departs from Tokyo Haneda Airport at 07:05 and arrives at Fukuoka Fukuoka Airport at 08:55.
The flighttime is about 1h 50m. The distance travelled ("as the bird flies"): 1048 Km. So the average speed is roughly 572 Km.
The best day to arrive at Tokyo is Sunday and it would be best to avoid Thursday, as prices are on average 333.5% higher than on Sunday. (Average prices, based on 3352843 datapoints.)
We have a lot more statistics for flights JL 305 and between Tokyo and Fukuoka.
