You can get around most of central Fremantle for free on the Central Area Transit CAT Bus which runs every ten minutes during daylight hours. It is orange with a large black cat on the side. Look for the CAT symbol at bus stops, and maybe even paw-prints on the footpath. The CAT Bus is wheelchair and pram accessible, including kneeling automatic lowering suspension and ramp access.
Alternatively, you can use your feet; most of Fremantle is fairly flat and good for walking or rent a scooter from Scootabout in Cliff Street.
For a local car hire, try Bayswater Car Rentals. They rent nice little cars at good prices. 13 Queen Victoria St, +61 8 9430-5300.