It is possible to use the same Apple ID for both devices (for purchasing and sharing apps and content), but use different iCloud accounts (for mail, reminders, calendar, and other iCloud syncing services). Sharing an iTunes Store account is allowed under Apple's ELUA, as long as it is for immediate family members. Kind of like taxes.
Using your Apple ID for Apple services
Under the App Store, iTunes, iBooks, and other store/purchasing apps, keep using your Apple ID.
Under Settings > iCloud set up a new Apple ID for your daughter. This will keep all your (and her) personal data separate. You can still choose to share specific calendars and reminders lists if you choose to; but they have to be set up explicitly in the apps (or at icloud.com on a computer).