Cruise lines generally don't (cannot) publish exact details of the 'sea lane' or precise route that their vessels will take as it is up to the Captain once he leaves port. All the skipper is limited to is departing at a certain time and arriving (at the next port) at a certain time, without burning up a lot of fuel. If the weather is bad, or currents are strong, or a certain strait or passage is too congested, or his girlfriend wants to wave to her mother onshore, the captain will alter course and speed as he considers necessary.
To get the best guesstimate, I would search for records of similar size ships transiting from Rabaul to Kagoshima or the reciprocal course.
Be assured though that 'the path the QE might take from Rabaul to Kagoshima' will be the shortest, and the most practical.
Good luck & smooth sailing