Rani Rose is a daddy’s girl!
The video — with “Not Alone” by Patty Griffin in the background — shows a soft-smiling Fujikawa, 32, caressing and kissing little Rani.
“Kind beautiful man, your pure love is such a gift,” wrote Hudson, 39, about her musician beau, hashtagging the post #daddysgirl.
The clip is the first post featuring Fujikawa with their daughter. On Friday as well, Hudson posted a photo on her Instagram Stories of a “nipple whip,” a cream meant to aid her sensitivity while breastfeeding.
“When life revolves around your nipples, literally,” she captioned the Boomerang.
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On Thursday, the Almost Famous actress shared an adorable photo of sleeping Rani in her arms. “The early morning calm,” she wrote.
A source previously told PEOPLE, Hudson, who is also mother of 7-year-old son Bingham Hawn from her relationship with ex-fiancé Matt Bellamy and 14-year-old son Ryder Russell from her marriage to ex-husband Chris Robinson — is over the moon about Rani.
“She’s always wanted a daughter so this is really a dream come true,” the insider said.
RELATED VIDEO: Kate Hudson and Danny Fujikawa Welcome Daughter Rani Rose — Find Out the Story Behind Her Name
The source added Hudson’s sons are just as elated. “Her big brothers are so excited— they’ll be protective and sweet to her always.”
After the baby’s birth on Oct. 2, Hudson explained the meaning of Rani’s name.
“We have decided to name our daughter Rani (pronounced Ronnie) after her grandfather, Ron Fujikawa. Ron was the most special man who we all miss dearly. To name her after him is an honor,” Hudson wrote on Instagram, referring to Fujikawa’s father Ron, who died in 2012.