The name reminds me of The Babadook, a critically acclaimed movie from last fall about postpartum depression / the horrors of childrearing. Not the greatest association, I'd think.
Interesting idea, but how is it different from note keeping apps ( like evernote ) ? Infact now that i think i can actually do stuff like this using a private instagram account.
The UI from the photos looks really nice though, i presume this isn't your first app.
Evernote is a great app for keeping notes, but it is more oriented towards professional use. This, on the other hand, is a memory book for babies where stories are organised into albums. The easy-to-use UI is focused on pictures and rich text information about babies' firsts, thus creating memories that last forever.