From the Science faculty handbook:
Transferring into the BPsych
Students may transfer from any degree into the BPsych with the permission of the Dean provided that they have completed at least 48 cps and have obtained a High Distinction average in at least 12 credit points of Junior Psychology units of study.
You don't have to be in the BPsych degree to be doing Psychology, you can still do the same units in other degrees that allow you to take Psychology units. You can still major in Psych in a BSc or a BA. And by the way, there's a new degree called BA(Psych) which is similar to the BPsych structure-wise, just that you do Arts subjects instead of Science subjects besides Psych.