I read this (English, medium-length) novel about 8 or so years ago, though the copy I received seemed a good few years older. I am Australian, so there is a higher likelihood that it was an Australian author. The cover was yellow, and featured the main cast of characters on it, most particularly (in my memory) an exaggerated cartoon tiger. The way the title was printed was also heavily exaggerated and stylised. I don't believe the novel was part of a series.
The story started with a suburban girl, who lived close to a dopey, female hippie neighbour. She found an animal (possibly a bird?) near her room, which displayed some unusual characteristics (I think it spoke), which ran off to the neighbour's house in question. She tricked the neighbour to let her into her house by telling her it was a 'help-a-neighbour day', or something similar, where she spent her time organising their record collection while looking for the animal. At this point the neighbour gave a speech on the topic of wanting everything to be free ("free booze, free love", quite heavily stereotypical). The protagonist eventually found the animal in the neighbour's house, with an indestructible letter in its possession. She was able to open and read the letter somehow, which instructed her to flush herself down the toilet, which she does (I also remember a passage describing a pair of combat boots she wears, and telling her mother that she's off on a long trip).
After flushing herself down the toilet, she finds herself in a fantasy world, which according to its inhabitants, is ruled tyranically by her old maths teacher (his name was something very intentionally generic i.e. 'John Smith'). From here, I don't remember much in detail, though I do remember that it followed a similar story structure to the Wizard of Oz, or at least aimed to parody it. The tiger on the cover I believe was a toothless plush tiger, which accompanies her in her adventure. I also faintly remember her defeating a number of enemies by kicking them specifically with her combat boots.
The story ends in a large magical conflict, or fight to the death, between the protagonist and her old maths teacher. I believe this ends in redemption as she demonstrates her mathematical knowledge to the teacher, and convinces him to stop his tyrannical rule. From there, I think the crown is passed to a totally inappropriate character (maybe the tiger?). The closing page of the book features an illustration of the characters singing The Internationale. I believe the translation given of this was:
So comrades come rally
[I can't remember this line well, perhaps ending in 'face']
Unites the human race
My attempts at finding the book as described above have been fruitless. I would greatly appreciate any clues, ideas or answers pointing me in the right direction.