"Can't wait to see the woman you grow up to be. I have a feeling you are going to be strong, fierce, compassionate, and caring. I'm so proud of you, Willow," Carey ended.
Fans soon flooded the comment section to both praise the forward-thinking parents, as well as pointing out Willow's resemblance to her famous mum.
Pink recently came under fire by mummy-shamers for dying her daughter's hair blue after trolls hit out at American actress and singer Jessica Simpson for allowing her young daughter to dye her hair a vibrant pink.
“I heard people were bummed on Jessica Simpson for letting her 7-year-old get her hair colored,” Pink wrote next to the snap, “So we thought we’d share what we did yesterday.”
Pink - who disabled the comments section on her photo - completed the post with hashtags including, “#bluehairdontcare”, “#getyourownkids” and “#ohlookmanocomments".