It has been a wild ride for a woman who, until last year, had never travelled overseas. "When I was finishing school and everyone was on their gap years, I was really jealous because I wanted to go to London and backpack around Europe, but I didn't have the money – or my family didn't have the money – so it seemed like a long shot," she says. The changes in her life have taken some getting used to. Only six months ago, she told Fairfax she would prefer to be in her back garden at home in Melbourne's Northcote than travelling. "I get overwhelmed very easily, and kind of anxious, so it's kind of nice to have that safety feeling of being at home," she says. Barnett grew up on Sydney's Northern Beaches and at 16 moved to Hobart with her parents. At that age, changing schools felt "like the end of the world", she says, "but it wasn't". Her mother, Cheryl Barnett (nee Mallinson), was a dancer with the Australian Ballet, while her father worked in staging and screen printing for the ballet. In her 20s, she moved to Melbourne and worked bar jobs while she wrote music. She met established singer-songwriter Jen Cloher and played on Cloher's third album before Barnett's own star began to rise. Now a couple, Barnett and Cloher have recorded a song, Numbers, about the 11-year age difference between them.

Barnett's songs are intimate, melodic and gently funny. A sample of her wit: "The paramedic thinks I'm clever 'cause I play guitar/I think she's clever cause she stops people dying" (Avant Gardener). In conversation, too, she frequently retreats to the safety of self-deprecation. She confesses that friends "take the piss" out of her everyday songwriting themes. They joke that she should write about the times she doesn't wear socks. "It's kinda funny," she says. "I don't care." Her voice has the ability to bring ordinary tales to life, but she describes it as "a balance between shit and average". "When I started learning guitar, I tried to sing along to [Nirvana]. But I didn't really sing when I was a kid, I was way too nervous about it – really kind of vulnerable. I never sang in front of anyone until I was about 18. Even then I'd try to sing and I'd get so nervous at gigs and open mics and stuff … I sounded like shit 'cause I was doing that wavery, nervous-voice thing. The first time she felt comfortable with her singing voice was when she heard her debut EP, the critically-acclaimed I've Got a Friend Called Emily Ferris, in 2012. The key was her discovery of a laid-back, casual style. "It works," she says. "I don't feel nervous with that coming out of my mouth."

Barnett is ordinary in the best way; she gives off the kind of calmness characteristic of people who make friends easily. She smiles broadly and spontaneously. Above all, she seems authentic – a trait that comes through in her songs. Still, although there is no swagger about her, these days she is far from unsure of herself. It took guts to release that first EP on her own label, Milk Records, which she runs with Cloher. The female artist she most admires is punk icon Patti Smith. But she would never tackle one of Smith's songs: "I could probably never perform a song like Patti Smith, with that intensity, 'cause I'm not strong enough mentally yet," she says. "My songs are very revealing in my own way." Barnett's delivery is appealing because people find comfort in it. Most listeners connect with her music first and her poetry later. Her tone is warm, with a disarming hint of vulnerability, her enunciation is sharp and she sounds Australian, which works in an age when indie music is less homogenous than ever.

She might play down her voice and project a loose, slacker persona but her songwriting is meticulous. She has been obsessed with writing lyrics since was 15. She remembers to the day when she started learning to write songs: "Grade 10 English class with Mr Cross. He got us to pull apart Paul Kelly's To Her Door ... We literally went through line by line. Like, why did he write 'silvertop', why didn't he say 'taxi'? I learned about the power of words." Another major factor in her success is the humour of her music. She draws influence from oddball Melbourne journeyman, Darren Hanlon, who sings with an arched brow as he tell stories that romanticise ordinary events. Barnett becomes animated at the mention of his name, and the sound born out of the Candle Records era in Melbourne, which heralded bands such as the Lucksmiths. She makes a point of mentioning Hanlon, and Melbourne four-piece Dick Diver, in overseas interviews when asked to namecheck other Australian bands. Her labelmates fit the mould too: the Finks, Royston Vasie and Fraser A. Gorman. "It's this perfect opportunity to go, 'I run this record label and these are my friends, and I think they're great musicians. Look at them, buy their music!' We don't have thousands of dollars for publicity, so it's kind of nice that it happens that way," she says. "I feel so lucky 'cause I've made friends here and become part of this Melbourne music community, which is incredible. It's encouraging – everyone supports each other." Barnett remains bemused that people in Switzerland, Italy and Spain want to know if her allergies, the inspiration for Avant Gardener, have settled down.

"I was a bit scared to go overseas, I thought maybe they wouldn't care. Not that they wouldn't understand; that they wouldn't care – a bit like, 'Why would I want to know about that?' "But then, so much of the American music we grew up with – and English music – people talking about walking down the streets in New York ... we still love it. You put yourself in that situation regardless of the place. It's more about the emotion." She no longer has to imagine what New York and London might be like; those cultural capitals are embracing her. Has she outgrown the safety of her suburban backyard? "When I say I enjoy being at home, I remember when an article came out [last year]. I got this angry email from some crazy person in the United States saying, 'You're so ungrateful! You're in a position where [you can travel]," she says, horrified at the memory. "That's so not true. I'm so incredibly grateful because of all the opportunities."

Courtney Barnett plays the Laneway Music Festival on Sunday. Her debut album, Sometimes I Just Sit and Think, and Sometimes I Just Sit, is out on March 20.