Nice concept, and best of luck developing it. I would second junto's comments on additional information, in particular sharing options.

This could be a perfect platform, for example, for my beautiful wife and I to share our (as yet, imaginary) baby pictures with close family who also have the App. My mother could then, in theory, open the App and have an album for each of her grandchildren instead of them being all spread out over Facebook and Instagram. I would value such as closed network more than the ability for me (or others) to share onto wider social networks.

Friends of ours have a 'Family Photos' dropbox folder with these sort of categories, by way of understanding the alternatives to your product. Clearly the additional story-telling and caption features in Babydook would give you the upper hand.