A good question.
A local answer.

Book a licensed transfer that confirms the infant seat type and installation in writing.

Call before booking to check availability, preparation and the price for the portion.

Independent travel gives flexible time at a few lookouts; a tour may cover more locations but spend longer in the vehicle.

Skip the excursion if the inbound flight is delayed; a harbour photo is not worth risking the onward ticket.

Check track alerts, weather and daylight before leaving, then keep a shorter loop ready if conditions change.

Allow a short walk from the venue; a slightly wider search often gives more room and better value.

Price airport rail against a car for all three passengers, including luggage and the hotel's exact location.

Choose one major outing per day and leave room for naps, meals and a nearby playground.

Start with a central shopping area reachable from the hotel, where several mainstream stores can be compared in one trip.

Give the Blue Mountains a full day with weather and mobility options rather than squeezing it into a city afternoon.

Leave enough time for the walk and theatre entry, especially when the meal is before a timed performance.

Check the match venue and the current rail timetable in both directions, allowing time from station to ground.