Marketing consumer apps is REALLY hard. I can't possibly overstate that. It's expensive as hell and requires a lot of hustle on your part.
The reason it's so hard is that consumers don't want to download apps and rarely do. So asking consumers to just download and try your app is hard enough, but you're actually asking them to pay for it ahead a time. That's a tall order.
I'll also give you some more honest feedback than others seem to have been. It's a great design and idea, but it's almost impossible to get people to create a new habit.
If people weren't already tracking their baby's every move, they're not going to start doing it now unless the benefit is really, really clear.
A good example is fitness/calorie tracking. That's something that a pretty large percentage of people bounce off of, and the reward is feeling better, living longer, and looking better. That's a pretty big reward, and it's still not an easy thing to get people to do. (Though I should note that people have actually been doing that activity for a long time.)
So this is a really steep hill for you to climb, and it may not be monetizable in the end. That's ok, though, because you're done a fantastic job so far and will always be able to point to this product to show that you can execute. That's really valuable for the rest of your career.
My suggestion, which a VC gave me years ago, is to choose metrics for success (number active users, dollars made, etc.) and choose a target date. If you don't hit a goal for those metrics by that date, walk away from the project. If you don't have a concrete way to cut yourself off, you'll allow hope to string you along forever. Trust me, I've been there more than once!