Who wouldn't want to be like Katniss Everdeen? Strong, kind and tough, the heroine of the Hunger Games trilogy wields a bow and arrow so brilliantly she beats all comers and foments a revolution. Boys and girls alike love her, which helped make the first film of the series a global hit last year.

Here, at last, is a brilliant role-model for tweenage girls: one who wouldn't be seen dead in a princess outfit in case it hindered her ability to run for her life, nor the sort of "and then my clothes fell off" fashion of so many computer-generated heroines (RIP Lara Croft). Jennifer Lawrence, who plays Katniss, refused to lose weight for the part and has spoken of the need for "strong and healthy" examples for young fans. In an interview on Newsnight last night the Oscar-winning actor said: "Kate Moss running towards you with a bow and arrow wouldn't be scary."

So imagine the scene as a group of toy manufacturers meet to discuss how best to capitalise on the latest movie in the franchise – Catching Fire, out 21 November, just in time for the Christmas gift guides. There are official badges and games and figures, of course, but what about the girls who really want to ape Katniss and wield a bow and arrow? And how about the parents who would love to buy toys that encourage outdoor play, rather than the makeup ranges and handbags that seem to start screaming at our daughters earlier and earlier?

Eureka, said the brains at Hasbro: let's produce the Nerf Rebelle range of toy weaponry for the "ultimate in girl-power outdoor play". The items – called the Pink Crush Blaster, the Guardian Crossbow and, yes, the Heartbreaker Bow – all come in pink, with prettily patterned soft darts.

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OK, so the Heartbreaker Bow isn't marketed directly at Hunger Games fans – partly because Hasbro didn't win the franchise rights, I suppose – but I can't think of many other reasons for the launch of a bow and arrow for girls this year. In a promotional video, a saleswoman dressed remarkably like Katniss shows off her target practice and speaks of accessories that allow girls to create an avatar. "You can play with the hair and face and shoes and clothes," she says, happily. People, crossbows are meant to help you survive, not look good on a catwalk.

Abi Moore, the founder of Pinkstinks, the campaign that managed to get Hamleys to stop branding beauty products and ironing boards with pink for girls while leaving the construction toys and outdoor games for the boyfolk, is also disappointed. "We are desperate for decent female characters in film. Then one comes along and you get this. What's so disappointing is that it has to be done in a pinkified, prettified way. It's overly feminised. Not that there's anything wrong with being feminine, but there's more than one way to be a girl. It isn't all about being pink and pretty."

That's the problem. I've got nothing against pink per se, and I'm happy to see it having a bit of a fashion moment for grownups. I'm tired of pointing out that pink was the colour of masculinity a long time ago – that there's nothing inherently feminine, or inherently problematic, about the colour. I also think that, in some ways, Hasbro should be praised for producing a toy for an "outdoor girl", rather than the makeup, jewellery, dolls and tea sets that sit them down inside the house. At last we have a female screen hero with the body of someone you could bump into in the supermarket and an aesthetic that suggests substance over style. But Hasbro appears to have taken this new type of girl hero and given her a marketing treatment that feels distinctly out of date – one that depends on being attractive, even when wielding a crossbow.

Both of my daughters want the "pink bow and arrow for girls" for Christmas – even the six-year-old, who isn't allowed to watch the films. Their older brother is dismissive, pointing out that a version marketed to boys – or, as he calls it, "the black one" – does more. Katniss, their hero, would agree with him.