Those in the army of devoted Peep Show fans who chortled through all seven series of the hit Channel 4 sitcom know very well that what we might call the "Dobby Years" are among the best.

A Dungeons And Dragons-loving IT supergeek, Dobby first appeared in 2008 and fast became an object of lust for David Mitchell’s character, Mark, and a cult fixture in her own right. She also features in Peep Show’s most celebrated line of dialogue: “Oh Dobby, let me chew on your weird hair!” spoken by Mitchell in one of his trademark voiceovers ahead of a messy frottage session in a stationary cupboard.

In the real world, where stationary cupboards are mostly free of canoodling oddballs, Dobby is 32-year-old actress Isy Suttie, whose parallel career as a singer, musician and stand-up brings her to Edinburgh this month with a one-woman Fringe show called Pearl And Dave. The production tells the story of a couple who meet once in 1997 and are reacquainted via the web eight years later. Suttie, who plays both Pearl and Dave, describes it as a mixture of stand-up and character drama, with some songs thrown in. Eight, to be precise. She talks about her own love life too, which she describes as “reasonably disasterous”. Perfect for the stage, in other words.

“It’s definitely the most challenging show I’ve ever written. I’ve tried to be brave with the choices I’ve made and I’ve tried to be as honest as I can be about how I felt about different relationships,” she says. “I’ve always been fascinated by hope in adversity but I don’t want to be cliched, so I always try to be as real as possible.”

In part, the show is also about the internet and the narrowing effect it can have on how people communicate. “I don’t really like the internet that much,” she admits. “I don’t mean that it’s evil. It’s not that black and white. But I think that for some people it’s not necessarily beneficial to spend a lot of time online. And I am really fascinated by the way people communicate online – especially when it becomes intimate – and the feeling of freedom it can give you.”

Pearl And Dave is the third solo show Suttie has taken to the Fringe, but the first since she joined the cast of Peep Show. Is it hard to step out from behind a character as well-liked and recognisable as Dobby?

“No, I never think of her when I go on stage. Ever. If people do, I can’t do anything about it. And I don’t want to talk about her on stage because that alienates people who haven’t seen Peep Show. Probably in five or 10 years people will know me as more of an all-rounder; it just happens to be Peep Show that put me in the limelight. That’s alright. I love doing it.”

Daughter of a piano teacher mother and a Scottish father (Edinburgh via Ayrshire), Suttie was born in Hull and raised in Derbyshire. Her early talent was for music. “My mum’s very technical, she doesn’t compose anything, whereas I’m the other way round – I don’t know the names of any of the chords so I make up names for them. There’s one I call Sugar which I know now is an F Minor. But I’ve called it Sugar since I was about 14, just to remember it.”

She studied acting at drama school in Guildford, intent on pursuing a career in musical theatre, but discovered that it was her self-penned comic songs and her ability in comedy roles that was winning her acclaim. Because of that, much is made of the comparisons between her and Victoria Wood. Even Suttie herself has been struck by the similarity in looks, background and subject matter. So, was Wood an influence? Not at all. “I’ve only ever heard a couple of her songs, the second quite recently,” Suttie says. “But I think I avoided her when the comparisons started, which they did quite early on, even before I started getting reviewed. My mates used to say it.”

Bigger influences were comedians Steve Coogan, in his Alan Partridge days, and Chris Morris, the elusive comedy brain behind programmes like The Day Today and Brass Eye, as well as the filmmakers Mike Leigh and Shane Meadows.

Peep Show returns next year for an eighth series after a hiatus which has seen writers Sam Bain and Jesse Armstrong win acclaim for their work on Morris’s political satire, Four Lions. They’ve also been filming Fresh Meat for Channel 4, a six-part comedy set on a university campus. As she once did with Channel 4 teen drama Skins, Suttie has acted as unofficial script consultant for the series.

Before that, however, Suttie is back on our screens in Scottish comedy institution Rab C Nesbitt. She plays an alcoholic teacher in the first episode of the returning series, due to screen in the autumn. “My dad was so proud of me,” she laughs. So how did she cope with the accent? She didn’t. “I can’t do a Scottish accent. I can’t, even though my dad’s Scottish.”

Well, actually that’s not quite true. “I can do a posh Edinburgh accent,” she adds. “But only when I’m drunk.”

Isy Suttie: Pearl And Dave is at the Pleasance Above until August 29 (not 15), 5pm