ABC News' Suzan Clarke and Sabina Ghebremedhin report:

Anna Nicole Smith lived a tough life that ended abruptly by accidental drug overdose months after she had given birth to her daughter, Dannielynn, and even though the girl likely has no memories of her mother, she's beginning to ask questions about her death.

Dannielynn, 5, accompanied her father on a recent visit to the Bahamas, where her mother and half-brother, Daniel Smith, are both buried.

"And, you know she said, 'Why did mommy die?'" her father, Larry Birkhead, said in an interview that aired today on "Good Morning America." "And I said, 'You know, they, doctors couldn't fix her. But if you're good … you'll get to see her someday.'"

Smith, a reality-TV star and former Playboy model who struggled with prescription drug problems, was found dead in a Florida hotel room Feb. 8, 2007. The official cause of death was an accidental overdose of nine prescription drugs, including Valium and Atavan. She was 39.

Her son, Daniel Smith, 20, died Sept. 10, 2006, three days after his mother gave birth to Dannielynn. He died after an accidental overdose of the drug methadone with the antidepressants Lexapro and Zoloft.

Birkhead had a relationship with the Smith, but had to go to court to get a DNA test proving he was Dannielynn's father. Several other men had also claimed paternity of the child. The ensuing legal battle made headlines across the world.

In the years that have followed, the media frenzy has calmed, and Birkhead has been focused on giving his daughter a stable, balanced life.

"I've always tried to make adjustments," Birkhead, 39, told "Good Morning America" co-anchor Robin Roberts. "We adjust to paparazzi."

Sometimes, he said, they use disguises when they go out, but sometimes they go to Kentucky - his home state - and are able to be "normal."

He shared what it was like to raise a child as a single father, saying he "never knew it was going to be this hard.

But it's also fun. "I enjoy every day and every day is an adventure," he said. "You wish you had a couple more hours in each day."

Birkhead told Roberts that Dannielynn was "as well-adjusted as she can be," and shares her mother's love of shopping and sense of adventure.

Asked whether he was concerned about what Dannielynn might learn about her mother's life when she gets older, Birkhead said, "I hope that she understands that no one's perfect and people have triumphs and people have tragedies. And her mom really … soldiered on and she came from nothing and she, you know, lived her dream.

"But I also want to make things a cautionary tale … and give her the tools that she needs to where she has the opportunities that her mother and Anna's son, Daniel, you know, won't have."

Anna Nicole Smith's troubles with prescriptions drugs were no secret. In an interview with ABC News in 2001, Smith acknowledged the seriousness of her drug problem. "I was on prescription pain medication and I was taking too much and I went into a coma for that," she said.

Smith turned heads with her beauty, and her daughter appears to have inherited her mother's looks.

Birkhead took his daughter to the Kentucky Derby in May, and onlookers were shocked to see how much the girl favored her mother. Birkhead said he wasn't prepared for the public's reaction.

"You know, it's weird when your child is five years old and trending … There's all these big stars that came and the next thing you know Dannielynn's picture is all over the place," he said, adding that the reaction was bigger than he had expected.

While all eyes might be on Dannielynn, she seems determined for her father to get some attention of his own, and is playing matchmaker, Birkhead said.

"She says, you know, 'Daddy, why don't you go get married?'" he said. "I said, 'Well, who do you want me to marry?'

"Well, why don't you marry Lady Gaga?" he said, laughing. "You know, I'm thinking, you know, down-home Kentucky girl and she's thinking Lady Gaga. So maybe we'll meet in the middle somewhere."

His daughter is so set on his being married that there's "not a week that goes by" where she doesn't raise the subject.

"She made a Mother's Day card at school and I said, 'Do you want to make it for your mom in, you know, heaven? And she says, 'Yes.' But then she brought it to me and she says, 'You can have it and maybe you can give it to your new wife.'"

Such moments serve to punctuate the loss she has already experienced in her young life. "You have to fill out school applications and say … 'mother deceased,' so the extreme highs and the extreme lows," Birkhead said.

The feelings of loss never fully go away, he added. "It's hard to move on in that way because you have this little 47-pound reminder of her mother walking around," he said. "And you have all these images that are still so much very alive that you have to deal with every day.

"I want to keep Anna's image alive in a positive way. She could light up a room. And now her daughter's taken her place and she's lighting up every room that she goes into, trust me," he said with a laugh. "I feel it every day."