Kate Hudson Cuddles Baby Rani in Early Morning Snap

Kate Hudson is continuing to share her love for newborn daughter, Rani Rose.

Early Tuesday morning, the mom-of-three took to Instagram to share a sweet snap of an early morning snuggle session, showing herself, partner Danny Fujikawa, and baby Rani all holding hands.

"Two hands are missing to complete this family portrait but it's far too early for my big guys," the 39-year-old actress captioned the photo, referencing her two other sons – 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.

Hudson and Fujikawa, who have been dating for a little more than a year, welcomed their first child together on Tuesday, Oct. 2, making the sweet announcement via the actress' Instagram account just one day later.

"We have decided to name our daughter Rani (pronounced Ronnie) after her grandfather, Ron Fujikawa," Hudson announced in the post. "On was the most special man who we all miss dearly. To name her after him is an honor."

"Everyone is doing well and happy as can be," she added. "Our family thanks you for all the love and blessings that have been sent our way and we send our right back."

In the weeks since welcoming little Rani, Hudson has been keen on sharing insights into her life with a newborn, frequently sharing sweet snaps of her little girl for her fans. The actress, who also kept fans up to date throughout her pregnancy journey, has even shared several snaps of Fujikawa tenderly caring for his firstborn, enjoying some daddy/daughter time with strolls outside.

On Wednesday, Nov. 7, just five weeks after giving birth, Hudson made her first public appearance as she celebrated her new role with the United Nation's World Food Programme during an event in Los Angeles. Joined by designer Michael Kors and Access' Natalie Morales, she didn't hesitate to speak about her life at home with Rani.

"I'm just starting to get the itch to get out a little bit more, but I'm enjoying every second," she said, according to PEOPLE, adding that Rani "is all girl. She's feminine" and that her mother, Goldie Hawn, is "very smitten" with her granddaughter.

As for who baby Rani takes after, Hudson said that "she's a Fujikawa. It's the cutest thing. When you love your partner so much, and you see your child look just like your partner it's like your heart melts."