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Dungarees are cool again. I know this because Kiernan Shipka, the girl Mad Men fans have watched morph from Don Draper’s cutesie pre-schooler to troubled teen Sally, is wearing them with a pair of pink patent kitten heels — ‘Louboutins, actually.’ And having already walked red carpets in Oscar de la Renta, attended Chanel dinners and sat front row at Ralph Lauren, this 13-year-old knows her fashion.

The cake we are decorating together in West Hollywood’s Duff’s Cakemix (a chic DIY cake shop full of long-suffering au pairs and their wards having compulsory fun with icing nozzles) is, she informs me, to be based on a Valentino dress from the spring/summer RED collection. And just in case I don’t get it, and start tossing Smarties about willy-nilly, Kiernan has a detail shot of the dress on her iPhone for reference.

This place is her ‘new obsession’, Kiernan tells me in her Valley Girl drawl, and she’s invited me along so we can get to know each other while enjoying an age-appropriate activity. When I arrive she’s already sitting at a workstation in latex gloves, with an intimidating array of baking accoutrements, looking extremely keen to get on with it. ‘Basically what we’re doing is daisies on the bottom then these textured bits are to go on the daisies. We’re going to do a rose on the top, and let’s keep with the white and yellow theme.’ She sets to cutting out marzipan flowers with the same steely determination I imagine brought her to LA in the first place.

Kiernan, an only child, convinced her parents Erin, a property manager, and John, a real estate developer, to up sticks from Chicago to LA for pilot season (when actors compete for parts in new shows from January to April) at the age of six. Yes, six. ‘Oh, it was all my idea,’ she admits. And as she politely but firmly orders bakery staff to ice the cake yellow ‘with a good even coverage please’ and bring more water (‘thank you so much’), I can see how Mom and Dad might not have been given much choice. But, she assures me, hers are not typical Hollywood parents: ‘Honestly they don’t care. They would totally support me if I wanted to stop acting and say, do something in science, which is never going to happen. I got myself into it.’

Within the first few months of arriving in LA, Kiernan was offered the part of Sally. ‘I just did, like, three auditions and then got the role. It wasn’t too big of an experience just because it wasn’t a show that anyone knew. No one even knew if it was going to be successful then.’ Mad Men has since won an Emmy for Outstanding Drama Series for each of its first four seasons and four Golden Globes. Despite a funding conflict that threatened to derail season five, filming for the final series — set in the 1970s with a 13-year-old Sally — will begin soon.

She couldn’t be further from her royally screwed-up character who has seen it all: in the latest series she witnesses daddy Don having sex with a woman (not his wife), she takes up smoking and is faced with a deranged intruder. In season four she was caught masturbating by her mother Betty. But Kiernan seems to take it all in her stride: ‘Through Sally’s eyes, not through mine, I think she thinks that marriage and love and all that is sort of an illusion, you know. The adults around her haven’t really set the best example. That’s her view.’

Kiernan is unnervingly mature, having spent the past seven years gadding about with Jon Hamm, January Jones and a cast of glamazons rather than a class of spoilt schoolchildren. She says that asking who she gets on best with on set is like asking her to choose between her best friends: ‘There are no divas. We’ve been together seven years and we all get on. If I ever got brattish, everyone would be like “What are you doing?” and I’d feel terrible…’ Try as I might I can’t get Kiernan to say a bad word about anyone or anything. Worst-dressed celebrity? ‘As long as people look as if they like what they’re wearing, I’m not going to criticise them. I respect everyone’s personal style.’

When I ask what her guilty pleasure is, she looks genuinely shocked. Obviously, I’m talking ice cream or trash TV. Not crack, I clarify. Still, the concept is anathema to Kiernan, although she did watch the US reality TV show Dance Moms for 45 minutes once. ‘I always like doing things that have a meaning. I don’t like wasting time.’

The intense filming schedule has meant no time for school, so Kiernan has a tutor and studies an online curriculum for three hours a day on set. She likes writing, hates science and is currently working on ‘a two-page essay about what life would be like if the atmosphere was wet, and it would be pretty boring because everyone would die’. Her friends are not other child actors but teenagers she’s met at sports and drama clubs, who attend different LA schools. ‘I have a lot of great friends so I don’t get lonely. I mean, sometimes I think I’d like to go to regular school but, gosh, people my age are so dramatic — it’s literally the most dramatic point, there’s so much drama. Even with my friends. It’s crazy to think that there’s a whole school full of these people. That would be crazy, I couldn’t handle it.’

Actually, I think she could. She has a black belt in taekwondo. ‘I like the discipline aspect of martial arts. It's hard, but I like knowing I can defend myself. It gives me another kind of safety net. I feel like it’s good to have that in my back pocket so I can throw it out whenever.’ When she’s not kicking ass, playing tennis, or rehearsing with her improv teenage comedy troupe (‘we’re called Detention Hall, but we’re changing our name’), Kiernan likes to brunch with her girlfriends. ‘No matter where we are it’s always good. Brunch is our Saturday thing.’ And at night, she dines out with friends: ‘I have a nice amount of restaurants I really like to frequent but I’m still looking for some new places... Do you have any recommendations?’ she asks. Umm, I doubt any of my ideas will cut it, seeing as her absolute favourite place to hang out is Chateau Marmont for its ‘old Hollywood vibe’. On the few times she’s been, she tells me, ‘I’m just thinking, “What can I Instagram now?” ’

Kiernan’s Insta-life is all cupcakes, pretty dresses, flowers and fashion, replete with smiley emojis, pink borders and love hearts. She posts a picture of our finished Valentino cake to her 12,000 followers, only to delete it a few days later on the grounds, presumably, of sloppy workmanship.

In her hyper-perfect world there’s no room for ‘I hate my life!’ door-slamming and pubescent rages. But surely there must be something of the stroppy teenager about her? I ask what posters are on her bedroom walls. ‘My room I get very nervous about. I like to keep it very clean. Every morning I like to make sure everything is in place, so my room is not the place for posters and pictures. It is very simple and compartmentalised.’ Sigh. She does at least admit to being a fan of teen idols including Emma Watson, Lana Del Rey and, oddly, Maroon 5.

After Mad Men, Kiernan is keen to break into movies like her idols Grace Kelly and Audrey Hepburn. She has ‘of course’ had offers, though nothing as yet confirmed. A side career as a fashion plate is already under way, although designing her own clothes seems unlikely: ‘I tried to make my own dress from scratch, but gave up when I realised I can’t even sew on a button.’

We’ve put the final rose on top of the cake (right). ‘Oooh, it’s so pretty,’ she coos. We joke she should take it to the Carolina Herrera party she’s going to that evening: ‘Ha, can you imagine — I’d be like, “Hi fashion people, I brought a cake!” ’ Kiernan would never do something so misjudged. I get the sense she's learned well from her on-screen mum January Jones, who is so notoriously private she has never revealed the father of her two-year-old son. Kiernan is as sweet as icing sugar and yet adroitly guarded: a good grounding for a career in Hollywood.

So is she looking forward to turning 21 and being able to go to wild parties without a chaperone? Again that killer ‘who me?’ look: ‘I don’t think that will be me ever, I’m not even thinking about that yet.’ After the interview her publicist emails to ‘reiterate that Kiernan is 13’. She hopes any ‘inference made to drinking isn’t part of the story’. Having spent an hour of controlled fun in Kiernan’s company it seems unlikely it will ever be.

Lindsay Lohan was cute once, but I bet she never had a closet categorised by clothing type and season. For now at least, this cheery, media-trained, perfectionist princess, who can render a man unconscious with a single blow, is having her cake — and eating it.

Photographs by Nicole Nodland. Styled by Nicky Yates

Hair by Bridget Brager at The Wall Group using Oribe Dry Texturizing Spray.

Make-up by Lauren Gott for Chantecaille