You can use product properties, to do this. An extra field will be added to your product at the cart and it will visible on your orders.
If you need more assistance please send us an email and we will respond ASAP.
You don't really need an App to do that, it can be done making some edits on your theme.
What do you want to do with the calendar? If you adding one to the product page, the date selected can be visible on the cart and also on your orders register.