When the new wave of feminism meets the thorny subject of child sexualisation, sparks fly. From worrying about Miley Cyrus and Rihanna as tween role-models to plastic-surgery game apps for kids, from children's TV presenters banned from wearing red lipstick to campaigns against pink, princessy toys, it seems barely a week goes by without heated debate over the images we feed young girls.

But alternative role-models are beginning to appear: ads for GoldieBlox, engineering toys for girls, were shown during the this year's Super Bowl, while in the UK, VIP (Very Intelligent Princesses) is a new website featuring fictional girls who like fixing things, playing games and having adventures (not a sparkly tiara in sight). British stages have seen a host of rewritten feminist fairy tales: from the RSC's Wendy & Peter Pan to a Doc Marten-wearing Cinderella at the Unicorn Theatre to Tom Wells's Jack and the Beanstalk where the hero was, in fact, a girl.

One performance artist goes even further: Bryony Kimmings's new show for children – created and performed with her niece Taylor Houchen, 11 – explicitly tackles the subject of the sexualised role models, and sees the pair inventing a new kind of pop star. Their creation, Catherine Bennett, is Kimmings dressed up in wig, glasses, knee-length skirts, and, yes, red lippy (she insists make-up is about personal choice, not objectification). The character is a "normal lady": a bike-riding, tuna-pasta-loving palaeontologist, who also happens to be a pop star. She sings bouncy, Lily Allen-ish songs about friendship and animals – but also about human rights and the vote. Target audience? Six to nine year olds.

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Kimmings, 32, from Hackney, east London, is bold in her aim to politicise her kiddie crowd: "I want to plant the seeds in their heads that they have power, they have rights.... To begin politicisation as young people, that excites me, rather than 'this is a nice story where we dance and sing....'"

That Catherine Bennett Show – part of the Southbank Centre's Imagine Children's Festival – is a new version of Kimmings's lauded, very adult, production Credible Likeable Superstar Role Model. In that, she explored, alongside Taylor, the dominance of Identikit, hyper-sexualised and commercialised acts such as Katy Perry and Jessie J, before delving into the darker recesses of the internet and what it looks like to a pre-teen. This filled her with fury – so she and Taylor decided to change it, with their alternative pop star. "The whole ethic of the Catherine Bennett project is: if you see something you don't like, change it, and if everyone put something good into the world, it would be a better place," says Kimmings, whose no-bullshit sass masks a tender, winningly hippyish idealism.

This new show is wholly age appropriate. The darker elements of the original are swapped for magic, silliness, and lip-syncing, as well as that "you can change the world!" message. "For adults, it's easy to say [we need new role models]... because everything is tits and arse and every woman is objectified. I've never told Taylor that's what it's about! [We've] always just talked about how pop's really limited, and wouldn't it be exciting if it didn't have to be like that?"

Taylor and her Aunty Bry have been on Radio 4's Woman's Hour and on Radio 1 with Gemma Cairney (she and Kimmings have also made a documentary about feminism with young listeners, to air on Radio 1 on 10 March). They visited the Houses of Parliament, will host a day of Camp Bestival this summer, while Catherine Bennett often goes into schools.

The character might be about to get her own TV show, too. Kimmings and Taylor – who as Catherine Bennett's manager, is very much in charge – are in talks with a production company. "We want it to be feminist, political," Kimmings explains. Catherine Bennett would sing songs, but not be a pop star (too Hannah Montana); instead, the show would focus on a magical museum. Early drafts feature a feminist exhibition that keeps taking over the museum, and a kid getting lost in space and pondering his own mortality. "It's pretty dark and deep," says Kimmings, "but I think that's what [children] need!"

Kimmings's previous shows, about STIs and binge drinking, were never going to be adapted for kids. Her next play is about rape and porn culture and its impact on teen relationships; starting the research has reignited her rage at the objectification of women. "I am angry, but I try not to be... that's new – I spent a lot of my twenties being absolutely fucking livid about everything. I think that change is Taylor."

'That Catherine Bennett Show' is at London's Southbank Centre until Tuesday