On Thursday, the actress shared a sweet photo to Instagram of her and Rani, snapped as the adorable baby slept in her arms. “The early morning calm,” Hudson, 39, wrote — hashtagging the post, “#babybubble.”
It’s the second photo of Rani that Hudson has shared so far. On Saturday, she posted the first picture of the tiny tot, who was fast asleep while snuggled inside a striped blanket and wearing an adorable pink hat adorned with a simple bow.
“Our little rosebud,” Hudson wrote in the caption of the picture.
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Hudson and boyfriend Danny Fujikawa welcomed Rani Rose, their first child together, on Oct. 2. Hudson is also the mom also mom to 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.
In her birth announcement, the mom of three explained the sweet meaning behind 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 said on Instagram (Fujikawa’s father, Ron, died in October 2012).
RELATED VIDEO: Kate Hudson and Danny Fujikawa Welcome Daughter Rani Rose — Find Out the Story Behind Her Name
Prior to Rani’s birth, Hudson said she and Fujikawa had yet to decide on a name for their daughter. “We have a couple of them and we’re going to decide when the day comes,” Hudson revealed during a Sept. 20 appearance on The Ellen DeGeneres Show with mother Goldie Hawn, 72.
A source recently told PEOPLE that the couple was over the moon about their baby girl and becoming parents together.
“She and Danny are great,” the source said weeks before Hudson gave birth. “Kate is bubbly with excitement every time she talks about Danny and how they are having a family together. She is crazy about Danny.”