You can email your baby's activities to yourself from within the app, and then print the email. That is the only way to do it currently.

Open the app, tap More and then "Share". Choose Printable format and what time period you want and then Send Email, that will launch your email app.

Or if you want to print the statistics screen or a chart go to the stats screen or charts screen, find the data you are interested in and press the Menu button on your phone and then tap "Share" or "Email".

Eventually Baby ESP will have an online site with easier ways to print off a quick report for the pediatrician.