Liv Tyler Gives Big Thumbs-Up to Her Father's Fiancee

Liv Tyler highly approves of her rock-star father Steven's choices – both in love and career.

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Asked about the American Idol judge's recent engagement to Clear Channel executive Erin Brady, Liv tells PEOPLE that she's an enthusiastic supporter of it, explaining that the two have been together "for a long, long time" and adding, "I like her very much."

Speaking to PEOPLE at the Sundance Film Festival, where she's promoting her new movie Robot and Frank, the actress, 34, also revealed that she's finally following in her father's footsteps – into the music business.

"I got to record a cover of INXS's 'I Need You Tonight' for a Givenchy commercial," says the model, who has a longstanding beauty contract with the European cosmetics company. "It was fun and terrifying and wonderful," she says of recording the song, which is due out soon.

It's a logical step for a woman whose roots are in music.

"I always thought when I was a little girl that I'd be a singer," she says. "My mom [Bebe Buell] was always in bands. My dad. And my stepfather, Todd Rundgren, is an incredible musician."

As for her dad's dicey performance of The Star-Spangled Banner on Sunday? Liv hadn't seen it yet. "Somebody told me my dad just sang the national anthem," she said. "I've got to go Google it."

Or, you know, maybe not.