For shopping you almost need one day. It's on Murraystreet downtown and another street (I forgot the name) with big stores. Next to the shopping center is the trainstation. Here you can take a train to Freemantle. They run frequently. Before the trainstation (in the shopping area) is the tourist information. Maybe you can find some suggestions for other activities or maybe other TripAdvisors can inform you in this. I wish you a nice stay in Perth.