I have just found out about this great charity organisation:
Bicycles for Humanity Western Australia (B4HWA) is part of an exciting global volunteer-run, non-profit organisation that uses donated bikes to help alleviate poverty through sustainable transport.
If you have any bike or spare components that you do not need, you can donate them to the organisation.
B4HWA has a number of bike drop-off sites around the Perth Metro area. In South Perth you can leave donated bikes at Garland Cycleworks Canning Highway South Perth (Junction of Berwick St).