Dakota Fanning Shares Throwback Photo of Herself at 2001 Premiere: 'Always Thinking of This Tiny Girl'

Dakota Fanning has some kind words for her younger self.

On Saturday, Sept. 21, the Perfect Couple star, 30, shared a sweet throwback photo of herself from when she was a 7-year-old child actor, attending the premiere of her first feature film, the 2001 drama I Am Sam , in which she starred alongside Sean Penn and Michelle Pfeiffer .

"i am sam premiere 2001. always thinking of this tiny girl, and keeping her close," Fanning wrote in the caption of her Instagram post, alongside a photo of her younger self wearing a yellow dress with a bow at the waist, white tights and black Mary Jane shoes.

I Am Sam followed Penn's character, a mentally disabled man raising his daughter (Fanning) who fights to keep custody of her. Fanning earned several accolades for her role in the film, including a Screen Actors Guild Award nomination for outstanding performance by a female actor in a supporting role and a Critics Choice Award win for best young actor/actress.

Fanning has previously been candid about her experience being a Hollywood star at such a young age. Back in June, she opened up to PEOPLE about what her advice for child actors might be.

"As long as you love it, you're in the right place," she said at the premiere of The Watchers, her thriller set in the forests of Ireland. "Sometimes you're working in a cold, wet forest, and if you can still have fun there, then you're on the right track."

Also in June, the actress spoke to PEOPLE about one of the strangest fan encounters she had as a child — and revealed how her mom, Hannah Joy Arrington , stepped in to help her avoid an uncomfortable situation.

"When I was young, somebody asked me to sign their chest or stomach," she recalled. "My mom was like, 'Oh, how about just a piece of paper?' "

Fanning's time as a young star also came with some nice perks. In April, she told Elle that the "best wrap gift" she had ever received was from one of her most famous costars, Kurt Russell .

" Kurt Russell gave me a horse ," she said with a laugh, before opening up about the making of their 2005 movie Dreamer, about a father-daughter duo who bond over helping an injured race horse.

"We made a movie about horses. Kurt is one of the loveliest, most amazing people," she continued. "You go through an experience together, and I loved working with him so much, and we made a movie about horses, and he gave me a horse."

She added at the time that working with other major stars — including Tom Cruise , Denzel Washington and Robert De Niro — was never intimidating for her as a kid.