Not being Australian, I did not try bikkies, but if I had, I would have assumed that the reason it was not accepted was because the singular is bikkie. This seems logical to me, because the diminutive "ie" ending appears to be much more common than the "y" ending in Australia. Google seems to bear this out, although it reveals other less common spellings, such as bikky, bicky, biccy and bickie.
I may be able to remember bikkie in the future, as I have already learnt the word brekkie.