Flight Haneda Airport departs from Tokyo Haneda Airport at 13:00 and arrives at Fukuoka Fukuoka Airport at 14:50.
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 Tuesday, as prices are on average 175.92% higher than on Sunday. (Average prices, based on 3138719 datapoints.)
We have a lot more statistics for flights JL 319 and between Tokyo and Fukuoka.