Rumer Willis Celebrates 'Our Girl' Louetta's 2-Month Doctor Check-Up: 'Can't Believe She's Mine'

Rumer Willis also posted a sweet photo of boyfriend Derek Richard Thomas and their baby daughter

Rumer Willis is celebrating every moment with her baby daughter.

On Wednesday, the new mom, 34, posted a few photos to her Instagram Story celebrating her daughter Louetta's 2-month check-up at the doctor. In the first photo, Willis' boyfriend Derek Richard Thomas, 28, holds a coffee cup in one hand and a baby carrier in the other while standing in an elevator.

"Baby Daddy looking like a snack....🌮," Willis cheekily wrote across the photo.

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Related: Rumer Willis and Boyfriend Derek Richard Thomas Welcome First Baby, Daughter Louetta: 'Pure Magic'

In the other photo, Louetta rests in her carrier on the floor. "Took our girl for her 2 month check up! I can't believe she's mine," Willis wrote.

On Father's Day this year, Willis shared a sweet photo of her daughter and her actor dad Bruce Willis, 68.

The photo, which happened to be the first of the grandfather and granddaughter, showed Bruce holding Louetta as he looks away from the camera.

"Fathers to the old and new. Seeing my father hold my daughter today was something I will treasure for the rest of my life. His sweetness and love for her was so pure and beautiful," Rumer captioned her post.

"Papa I’m so lucky to have you and so is Lou. Thank you for being the silliest, most loving, coolest Daddio a girl could ask for. Best Girl Dad in the game…."

In the post, she also celebrated her boyfriend, who is also a first-time parent. "@derekrichardthomas Happy 1st Father’s Day. Thank you for building a beautiful garden for Lou to play in and eat from. 🌱," she continued her caption.

"Thank you for filling the house with music for her to hear 🎶 Thank you for all the late night diaper changes and silly faces. I’m so grateful our girl has a papa that loves her so much and someone so goofy and weird so she knows that’s ok for her to be too. Thank you for the greatest girl I could imagine in my wildest dreams. We love you 🧡"

In April, Rumer told PEOPLE she couldn't help but wonder what her baby would be like — and specifically if they'll share the natural "goofiness" she inherited from parents Bruce and Demi Moore, 60.

"We're a family of weirdos, and I love that so much. I really hope that that is engendered in this child," she told PEOPLE. "That's my favorite thing, laughing with my family."

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