Is it ok to write a professor again who did not reply me yet?
Yes, it is ok to write again. Say you hope she is still interested and hope you can discuss the project soon. You could even suggest one or two days that it would be convenient for you and ask for alternatives. If you have applied, say so.
A week isn't a long time for academics, but it is long enough that a follow up won't be insulting. I wouldn't even mention the earlier mail.
This might not work everywhere, but I think Australia tends to have a fairly informal culture, like the US.