And the doting mum recently shared a relatable parenting update about being a busy parent.
Taking to Twitter, the Smile hitmaker wrote: "What did mothers do before Amazon Prime?" along with the hashtags, 'not an add' and 'just a fact'.
While Katy has so far been keeping photos of Daisy out of the spotlight since her arrival, the doting mum has been posting some sweet pictures of the gifts her famous friends have bought for her daughter.
VIDEO: Take a look inside baby Daisy's nursery
Most recently, Taylor Swift sent Daisy a hand embroidered blanket which had the words 'Baby Bloom' hand-stitched alongside a flower.
Katy Perry has revealed just how busy she is following Daisy's arrival
Beyoncé sent Katy and Orlando a beautiful bouquet of white roses, while Moschino's creative director, Jeremy Scott, sent Daisy a gorgeous red pram embellished with Minnie Mouse ears.
The Smile hitmaker a month before Daisy arrived
Katy and Orlando announced Daisy's arrival via UNICEF - they are Goodwill Ambassadors for the charity - sharing a black and white image of their newborn holding onto her dad's finger.
They said they were "floating with love and wonder from the safe and healthy arrival of our daughter," adding that they feel "lucky" and "grateful" to have been able to deliver their child so peacefully.
Baby Daisy has an incredible nursery at home in LA
Prior to Daisy's arrival, the Hollywood star revealed in an interview published in HELLO! that his son couldn't wait to meet his sister.
He said: "Flynn couldn't be more excited to be getting a little sister – he's already got two brothers from Miranda. So although the circumstances are definitely unusual, this is a wonderful time for us."
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