My five-year-old insists that Bilbo Baggins is a girl. The first time she made this claim, I protested. Part of the fun of reading to your kids, after all, is in sharing the stories you loved as a child. And in the story I knew, Bilbo was a boy. A boy hobbit. (Whatever that entails.)

But my daughter was determined. She liked the story pretty well so far, but Bilbo was definitely a girl. So would I please start reading the book the right way?

I hesitated. I imagined Tolkien spinning in his grave. I imagined mean letters from his testy estate. I imagined the story getting as lost in gender distinctions as dwarves in Mirkwood. Then I thought: What the hell, it's just a pronoun. My daughter wants Bilbo to be a girl, so a girl she will be.

Download the new Independent Premium app Sharing the full story, not just the headlines

And you know what? The switch was easy. Bilbo, it turns out, makes a terrific heroine. She's tough, resourceful, humble, funny, and uses her wits to make off with a spectacular piece of jewellery. Perhaps most importantly, she never makes an issue of her gender – and neither does anyone else.

Despite what can seem like a profusion of heroines in kids' books, girls are still under-represented in children's literature. A 2011 study of almost 6,000 children's books published between 1900 and 2000 showed that only 31 per cent had female central characters. While the disparity has declined in recent years, it persists – particularly, and interestingly, among animal characters. And many books with female protagonists take place in male-dominated worlds, peopled with male doctors and male farmers and mothers who have to ask fathers for grocery money (Richard Scarry, I'm looking at you). The imbalance is even worse in kids' movies: Geena Davis' Institute on Gender in Media found that for every female character in recent family films, there are three male characters. Crowd scenes, on average, are only 17 per cent female.

More insidiously, children's books with female protagonists sometimes celebrate their heroine to a fault. Isn't it amazing that a girl did these things, they seem to say – implying that these heroines are a freakish exception to their gender, not an inspiration for readers to follow. Children's lit could benefit from a Finkbeiner test. (Well-intentioned kids' media can, ironically, introduce their youngest listeners and viewers to gender barriers: The first time my daughter heard the fabulous album Free to Be... You and Me, she asked: "Why isn't it all right for boys to cry?")

So Bilbo, with her matter-of-fact derring-do, was refreshing. With a wave of my staff, I turned Gandalf into a girl, too, with similarly happy results. I started to fool around with other books and their major and minor characters, sometimes by request and sometimes not. In The Secret Garden, Dickon, the animal-loving adventurer who rescues Mistress Mary, became Mary's best friend Diana. In the Finn Family Moomintroll books, the Snork Maiden and her brother the Snork traded genders. In the Narnia series, Peter Pevensie and his sister Susan made the pronoun switch. (That was a nice fix for the infamous line about Susan's abandoning Narnia for "nylons and lipstick and invitations".)

Friends tell me that they pull similar tricks while reading to their sons and daughters: Women who farm become not "farmer's wives" but "farmers". Male animal characters become girls, and vice versa. Sleeping Beauty goes to MIT. Their kids, boys and girls alike, get to hear about a world as full of women as the real one – and as free of stereotypes as we'd like ours to be. Kid-lit may be catching up to our kids, but we don't have to wait for it.

My daughter might forget all about the heroines and heroes she helped create. But she might not. I hope that years from now, when she has a chance to take her own unexpected journey, she'll remember the story of Bilbo – and be a little more inclined to say yes.