I'm assuming this is a case where Princess is offering this to other people. If so, if you arrive early you would be able to drop your luggage off early, There should be Princess staff in the area that can provide you with current timing info. If embarkation is set at noon, then check-in would at least be a bit before that.
I don't remember the process, but the passengers on the ship need to clear Australian immigration so depending on how that is done, that could be part of the delay.
Worse case is drop off luggage and go for a walk.
As a port day for most passengers it would be very doubtful the dinning room would be open for lunch