Moore and her husband, Taylor Goldsmith, are also parents to sons Gus and Ozzie

"One whole month with our Lou. The hungriest, sleepiest, happiest, crusher of tummy time," Moore began her caption. "She's a total dream in every way and we can't imagine a world without her... like she's always been a part of the fabric of our family."

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The actress also gave her doctor, nurses and doula a shout-out for taking care of her and Lou.

"Forever grateful to the world's best OBGYN, Dr. Hadar Waldman, our excellent L&D nurses Rachel and Justice and our extraordinary doula @rebeccacoursey_photosandfilm for helping her meet us earthside. 📸 also by @rebeccacoursey_photosandfilm 💓💓💓💓," she wrote.

Moore and husband Taylor Goldsmith welcomed Louise in September. "Louise Everett Goldsmith arrived happy, healthy, expeditiously and right in time for Virgo season," the proud mom shared on Instagram on Sept. 25.

Related: Mandy Moore Has Skin-on-Skin Time with New Baby Louise: 'Doesn't Get Any Better'

"She is our absolute dream girl and her big brothers are already as obsessed with her as we are," Moore continued. "Endlessly grateful for our family of 5 (and our very own big three) and soaking in every moment of this special time. 💓💓💓."

Moore and Goldsmith, 39, are also parents to sons August "Gus," 3, and Oscar "Ozzie," 1.

Ahead of Louise's birth, the Tangled actress spoke to PEOPLE in June about the "biggest difference" being pregnant with her third child. This time around, she said she was "just chasing two wild toddlers."

Related: Pregnant Mandy Moore Says Third Pregnancy Has Been 'Hardest by Far' as She 'Chases' Her Two Toddlers Around

She also reflected on the transition to a home with three children. "It's so much fun. I know that parents sort of love to say it just gets better, but I truly believe that is the case," Moore said. "We have one that's obviously potty-trained and the other's still in diapers, but they're only 20 months apart so they're just starting to interact with each other."

"My husband I looked at each other the other day and we're like, 'This is a good phase.' But also recognizing in parenting, it's an ebb and flow," she continued.

"You cannot get used to anything because as soon as you sort of digested it and you're like, 'Oh wow, we can handle this,' then some other challenge is thrown your way," Moore added.