Hi, achewsky : )
I think someone has already made a tutorial for this hat (or something very close to it). Check this link
. You'll need to start with this video for the basic beanie
, and then the other tutorial will show you how to make the butterfly. The one here is not a newborn size, but all you need to do is adjust the number of stitches.
Edit: these videos use half double crochets instead of double crochets like the written pattern there. However, I made one using double crochets so it's just a matter of preference. If you want to use double crochets, she has this video
for the first part of the hat.
She also has tutorials on sizing for newborn through adult.
Good luck with your project!