Taylor Swift: A young singer's meteoric rise

Music sensation Taylor Swift writes and sings all her own songs, sells millions of records and she's just 21 years old

She started thinking Shakespeare...

Taylor Swift: And I got this pre-chorus in my head that said, "You were Romeo, you were throwing pebbles and my daddy said stay away from Juliet."

She raced in to work out the chords on her bedroom floor...

Taylor Swift: Maybe it's-- (sings it with right chords) and you're just like, oh, okay, well that's that.

[Music video - "Love Story"]

Taylor Swift: I had to fight for that song. Because when I first played it for, you know, my family, a few people-- they were just sort of like eh-- (makes noise).

Lesley Stahl: But you believed in it. You trust yourself.

Taylor Swift: Yeah, it's almost more fun that way when-- when you have something to prove.

"Love Story" went to number one on both Billboard's country and pop songs charts: the first song ever to do that. Proving doubters wrong is a big theme in the tale of Taylor Swift.

She started singing when she was still a toddler. She fell in love with country music and not as a coal miner's daughter from Kentucky. She's a stockbroker's daughter from Wyomissing, Pennsylvania - who at age 10 began nagging her parents to take her to the mecca of country music.

Taylor Swift: It was just on repeat. Just like a loop constantly. Like, 'How about we go to Nashville, can we go to Nashville, can I take a trip to Nashville? Hey.' So I looked up this tourist brochure about Nashville. 'Can we go see Nashville?'

Spring break 2001, they finally gave in and headed to Mecca, says her mother Andrea.

Andrea Swift: We started driving up and down music row. And at that point, she would say, 'Mom. Mom, pull over. That's Mercury Records. Let me out!'

She was 11, toting CDs of herself singing karoake songs.

Lesley Stahl: And she'd run in?

Andrea Swift: She would walk up to the receptionist, and hand them a demo CD and say, 'Hi, I'm Taylor. I'm 11. I want a record deal, call me.'

Lesley Stahl: Anyone call?

Andrea Swift: No. Sadly, no.

She spent the next few years performing every chance she got - even in a bar when she was 13.

Taylor Swift: I remember there was all these like rock-n-roll dudes and like biker guys. And I'm like, "This is a song that I wrote about the guy who sits next to me in class." And it was just like, you know, sometimes i ended up in the wrong venue. But it was still-- it was learning to talk to a crowd, regardless of whether it was the crowd that's going to be most susceptible to liking your music.

Somebody at RCA Records liked her music and offered her a one year development deal. That's when the Swifts moved to Nashville. Taylor was finally where she belonged. Or so she thought.

Taylor Swift: I would go and turn in songs, and more and more, I would just get suggestions that I write-- that I sing other people's songs. And, you know, I just didn't want to.

Andrea Swift: And at that point she said, 'My contract's coming up, Mom, I need to just walk.' And I thought, 'You're kidding.'

Lesley Stahl: How gutsy was that for a 14-year-old?

Scott Borchetta: Gutsy? No, how 'bout unheard of?

Scott Borchetta was an executive at another label.