For the first time since announcing her interest in assuming Hillary Clinton's Senate seat, Caroline Kennedy opened up in an exclusive NY1 interview Friday about her qualifications for high office as well as private reminisces of her family.

In her 30-minute conversation with NY1 political anchor Dominic Carter, Kennedy discussed her father, President John F. Kennedy, and discounted criticism that she's running on her family’s fame.

"If my last name weren't Kennedy, maybe I would have run for office a long time ago," she said.

Caroline Kennedy lived as a private citizen for most of her life, but her campaign support for President-elect Barack Obama threw her into the middle of politics in Washington, D.C.

"I think I have relationships in Washington that I would like to put to work to benefit the people of New York," she said. "I helped run the vice presidential search for Barack Obama, I have a good working relationship with him."

Kennedy said she is relishing doing the grunt work often associated with elected office, and said, “I could race [New York senior Senator] Chuck Schumer around all 62 counties and, you know, we'll see who wins.”

Caroline Kennedy gave no preconditions before accepting NY1's interview, and freely discussed what some critics have said about her.

She said she was “dismayed” to learn that she had missed voting in several elections and Democratic primaries, saying, “There isn’t a good excuse.”

Earlier this month, Queens Democratic Congressman Gary Ackerman derisively likened Kennedy to little more than a celebrity like Jennifer Lopez.

Kennedy responded, “I admire the journey J. Lo has traveled. I’ve been to a school in the Bronx near the house she grew up in and so I actually have a lot of admiration for her, and she looks pretty good. But in terms of public policy and how we spend our adults lives, I don't think there is really much we have in common.”

With Mayor Michael Bloomberg being a vocal supporter of Kennedy's serving in the Senate, she was asked about what she would endorse the mayor's race for a third term. She remarked that the mayor is "doing a good job," but said she is "a loyal Democrat."

Kennedy also discussed her parents, and in particular opened up about memories of her father's assassination.

She even discussed what she thought her late mother, Jacqueline Kennedy Onassis, and late brother, John F. Kennedy Jr., would think about her wishes to serve in the Senate.

Caroline Kennedy said of her mother, "She would roll her eyes about the whole thing, but she was an incredible patriot herself and I think she would be really proud that I’m doing this."

Thinking of her brother, Kennedy smiled and said, “Well, he would be laughing his head off, there’s no doubt about that, because that was the kind of relationship that we had. But he’d be 100 percent behind me. It’d be great if he was here."