Thanks to Australian Online Bookshop, I was finally able to track down a copy of this book, originally published by Spinifex Press in 2001. It's described as a comic crime novel.
From the Blurb:
When the ghostly Fedora interrupts Julie Bernard's coffee in Brunswick Street, Julie's life is set to change.
I was in one of those grumpy moods when burning your fingers on the caffee latte glass is no longer pleasurable. That day I hated everyone - even Jodifosta, my beautiful blue heeler puppy.