I've got my eye on you

Rumer Willis is ready to accept the ’round-the-clock responsibility of being famous. Presented over the weekend with a Rumer Willis Polly Pocket Doll – which she helped auction off for $5,500 to charity – at the Children Affected by AIDS Foundation’s annual Dream Halloween benefit in Santa Monica, Calif., the 19-year-old (and eldest) daughter of Bruce Willis and Demi Moore, joked, “I feel like I’m really famous now.”

But when it really comes to the fame game, Willis – who has become a gossip-blog fixture in recent months – tells PEOPLE, “Before I started working, I would have said, ‘You know, it’s not really fair, because I didn’t choose this.’ But when you decide to be a part of this profession and put yourself out there, then you kind of have to accept what it is.” Willis says that her famous parents – including stepdad Ashton Kutcher – aren’t worried about her, even though being a celebrity means having a very public life. “I think they know that I’ve had great role models,” she said.

Still, notoriety does offer its obstacles. “It’s a 24-hour job,” she says. “It doesn’t matter if you are going out to a restaurant – you have to be aware of what you are doing and how you look and how you are presenting yourself, because most of the time people never get to know you.” But at its heart, she says of celebrity, “Being famous isn’t going to parties … it’s about being able to use the power that we all have to kind of give back.”