I don't know whether you could call this image cutesy, though!
I read Blinky Bill once, perhaps twice when I was a kid, and the cutesy images aren't really what I remember. I think I identified with the Blinky character, who was usually getting into scrapes and/or trouble. They were very witty, too - the one line I remember from Blinky Bill is the comment Blinky makes when a friend loses his shoes: 'His feet have just dropped off.'
This one that I found yesterday just about sums up the meaning of Blinky Bill for me - the combination of childish innocence and childish delight in things that are just a little bit off:
As a glance at these images, on Project Gutenberg, will show, the books were also full of odd fantasias, derring-do, pure evil, stern patriarchal figures, fun, pathos, delightful characters, chaos, greed, and shameless sadism. The Blinky Bill stories were written and illustrated by Dorothy Wall, evidently a lady of many talents. You can read all about Ms Wall and her talents here, but I think this illustration says more about her - and with more wit, too.
Norman Lindsay's famous illustrated book for children, The Magic Pudding, is probably just as iconic as Blinky Bill, (although I doubt that people outside Australia would know anything about either of them.) Like Blinky Bill, the book was about a peripatetic koala bear, 'Bunyip Bluegum', although the real star of the book was the Pudding. The Pudding was called Albert, walked, and spoke, but this wasn't what made it magic. Albert was magic because he* was a 'cut 'n' come again puddin''. Which meant you could keep on eating him, and he would never diminish in size.
Maybe this is what made him so cranky:
Clearly, this cantankerousness has had some impact on his later reputation in literature!
The Magic Pudding was a great book. It had adventure and humour aplenty, and at the end of every day, the characters would all sit around and eat Albert thoughtfully while digesting the events of the day. There were also plenty of songs and slapstick, making the book a wonderful, wonderful classic.
I also got a copy of Snugglepot and Cuddlepie when I was a kid. Written and illustrated by May Gibbs, the book was a story of 'gum-nut babies' who were always under threat of being kidnapped by those Banksia men. May Gibbs characters were mostly plants (albeit plants that talked and walked), but the stories stretched from land to the depths of the ocean: they were great!
I suppose you could make a case for these sort of stories about native animals and plants (or puddings) being given arms and legs and clothes as a kind of environmentalism. You know, the authors anthropomorphise wildlife because it's easier for us to sympathise with them that way. I enjoyed the adventures and romps the characters got into more than anything else (and, in the case of The Magic Pudding, the idea of eating one of the characters rather appealed to my ravenous child-self.)
There were other books, including Dot and the Kangaroo, which were later turned into a whole swathe of films that we were made to watch at school. Pre-eminent in the genre is perhaps Lindsay's The Magic Pudding, but there are plenty of other, similar books that have their place in the scheme of things.
I'd be rather curious about international equivalents to these books. When I was in the States, I picked up one of the Freddy books, about a clever pig who lives on a farm. I think it might be somewhere in Iowa.
*Albert is a boys name, though I'm not sure if gender distinctions apply to puddings...