The troop capacity might be less, but IIRC the Karel Doorman has ~twice the lane metres of a Bay-class LSD. So the question would be, are you looking to move troops, or vehicles/kit? One of the other big differences is the ability to transport & support six NH90 or similar sized medium lift helicopters. Plus of course all the fuel, cargo, potable water, etc. from the replenishment side of the vessel.
As for the Dokdo-class LPH... I do not know how good a fit that would be for the RAN. It has a personnel carriage capacity similar to the Canberra-class LHD, and can move a significant number of vehicles (200 or so) but only something like 6-10 tanks. Relating to the large number of troops able to be lifted, for how long can the troops be safely and comfortably embarked? If memory serves, the LHD's can have troops embarked for ~50 days. Given that the LHD displacement is about 50% greater, with similar listed capacities for a number of things, I suspect the LPH could not support ADF personnel embarked for that long. Plus the crew requirement is over 300, which is about 50% greater than one of the LHD's, and about twice that of Choules.