What influences the movement (speed and direction) of tropical cyclones?
Cyclones generally drift in a westerly/north westerly direction due to the Beta Drift  and Beta Effect

For atlantic hurricanes the forward speeds are summarized here by latitudinal range -Average forward speed of Atlantic Hurricanes and  if there is recurve(turn more northerly) they can slow down or if they cross mid latitudes they may pick up speed by interacting with mid latitude troughs. 

For the latitude of Midge Point, Queensland you can expect forward speeds of about 17-18 kms/hr. So this cyclone is certainly slow moving. 

TC forward speed

There are other factors influencing cyclone tracks which include steering winds, presence of high pressure systems,etc and more recent studies have studied the influence of SST on cyclone tracks Response of  cyclone tracks to SST.

From this peer reviewed reference Effect of forward speed on flooding modeling studies reveal that increasing forward speed decreases flooded volumes while increasing peak surge

Back to Cyclone Debbie it looks like from this blog at least Cyclone Debbie Progress the forward speed of the cyclone is probably one of the reasons for the water to be present for more than one day and making sure storm surge occurs at the same time as the high tide.