I must have an Australian sense of humour, because it’s usually Australian books that make me laugh. The Terrible Underpants by Kaz Cooke (Viking pound;9.99) cracked me up. It’s a picture book for Reception and above, about Wanda-Linda, her pet hairy-nosed wombat, and her least favourite underpants.

One morning, when Wanda-Linda gets up, there are no underpants in her drawer. That’s because Dad has hung them all on the line. Which means she’s going to have to wear “the terrible underpants”. A fully labelled diagram shows us what they’re like, in all their dishevelled drabness. Wanda-Linda doesn’t believe Dad when he tells her no one will notice. Just how wrong Dad proves to be is at the heart of this hilarious book.

Imagine an appendix in a jar. How did it get there? What’s the story behind it? It’s another Australian book, of course: Sucked In by Paul Jennings, illustrated by Terry Denton (Puffin pound;3.99), for Year 3 and above. In this case, the appendix belonged to Trevor, a boy who had it removed in hospital, asked for it to be put in a jar, and vowed that he and it would never be parted. His mother and his school are not so sure, especially when the appendix begins to move around. Its movements become increasingly agitated whenever Trevor and the jar become separated. Jennings makes hay with the potential for slapstick as the appendix evolves into a monster on the rampage, swallowing cats and dogs. A funny story, with colourful illustrations, that provides the perfect invitation to variations on a theme.

In Archie Hates Pink by Karen Wallace, illustrated by Barbara Nascimbeni (Macmillan Children’s Books pound;9.99), Archie is a big orange cat with strong views about colour. Which is just as well, as he lives with a painter called Tallulah. Archie likes most colours, but he cannot abide pink. Pink is the colour of his flea-powder bottle, of the handle on his spiky brush, and of his medicine. When Tallulah decides to paint the whole house pink, Archie leaves home. He is shown some sights by a well-travelled black cat, Max, including the pink inside of a watermelon, a pile of pink shrims, and a bouquet of pink carnations. The story and illustrations combine to make this a joyful celebration for Year 1 and above of how our sensibilities can be educated and guided into a broader appreciation of the world.

Beetle In The Bathroom by Brian Moses and Sonia Holleyman (Puffin pound;4.99) is a rhyming story for Reception and above, about the host of insects who take possession of the bathroom. Moses’s rhymes - “A beetle was singing songs in the shower, He must have been there for over an hour” - are brightly illustrated by Holleyman’s artwork, making this a “read aloud and show pictures” book. Children will love the picture of the centipede cutting his nails and of the ants skating round the plug-hole.

Two other picture books are worth mentioning. That’s Not Fair, Hare! by Julie Sykes and Tim Warnes (Viking pound;10.99) is a witty and original slant on Aesop’s fable “The Tortoise and the Hare”. In this version, for Year 1 and above, the hare wins the first race, but the tortoise suggests they race again, with “home” the finish. Can you guess how tortoise wins?

Don’t Make Me Laugh by James Stevenson (Red Fox pound;4.99), for Year 2 and above, challenges the reader to remain straight-faced throughout the book - if you don’t, you have to go back to the beginning again.

Bill is a show-off. He likes to clown around, imagining himself as “The Great Bilbo”. In It’s Not Funny! by Jan Page (Corgi pound;3.50), he drives his mum and his teacher, Miss Carter, to distraction. Tony Ross illustrates just how naughty Bill can be in inimitable fashion. The young rascal gets something of his come-uppance when he is taken to a circus. While his mother is away from her seat, Bill goes into the ring and begins to perform his act. Initially the audience loves it, but Bill goes over the top and suffers a leg injury. By the end of the book there are signs that he is learning when not to be funny.

More short humorous fiction for Year 2 and above can be found in The Walker Book of Funny Stories (Walker pound;3.99), an entertaining collection which includes stories by Vivian French, Robert Leeson, Michael Rosen, Brian Patten and others.