A good question.
A local answer.

For wildlife and an island feel, allow a full day or overnight for Rottnest and arrange transport ahead.

Make it a half-day with one main stop and an easy train back, leaving room for a spontaneous find.

Expect downhill and an uphill return if you walk both ways, and check the crossing and footpath near the boat house.

If you hire a car for only part of the week, use those days for harder-to-reach nature stops. Keep central and Fremantle days for walking and public transport.

Look for a tour that states its public-transport meeting point and return time clearly. River cruises or coastal activities can be easier without a car than a remote beach excursion.

Check each venue’s current programme, admission conditions and opening times before going. The older forum link refers to a past touring exhibition, so use the venue’s own calendar to decide what is actually on during your visit.

Treat Wadjemup / Rottnest Island as a full outing if you want to cycle and stop at beaches. Compare the ferry port and timetable with your accommodation, choose a bike or island bus plan that matches your energy, and check weather before locking in the day.