Hi AmyFL,
Welcome to the Support Communities!
If I'm understanding your question, both you and your daughter are using the same Apple ID (which is an email address) for your iTunes Store purchases as well as your iCloud (contacts, calendars, etc.?)
Do you have one User Account (iTunes Library) on your computer or separate user accounts?
The article below will explain in more detail ... but it sounds like you need to create an Apple ID for your daughter for iCloud - for her own contacts, calendars, Photo Stream etc. If your daughter has a different primary email address than you, she can use it for her Apple ID.
If you have made a lot of iTunes Store purchases, she can stay signed in to your current Apple ID to have access to them. Or she can start fresh with her own Apple ID and purchases. Please review the information below including the Frequently Asked Questions.
I'm including the steps below based on this scenario. If your situation is different, or you are not clear about these instructions, contact AppleCare by phone or make an appointment with a Genius at your local retail store.
Using your Apple ID for Apple services
http://support.apple.com/kb/HT4895
Click on the link below and then click the "Create an Apple ID" link for your daughter:
Apple - My Apple ID
https://appleid.apple.com/cgi-bin/WebObjects/MyAppleId.woa/
Make sure that the email address she wanst to use for her Apple ID meets these conditions:
- The email address is one that she uses regularly, because it will be the primary email address for her Apple ID.
- The email address is not associated with any other Apple ID.
The email address is not an iCloud email address, which is already an Apple ID. iCloud email addresses end with @icloud.com, @me.com, or @mac.com.
iCloud: Change iCloud feature settings
http://support.apple.com/kb/PH2613
Before you delete the iCloud account from your daughter's iPhone, turn off each of the features ( contacts, calendars, etc. ) and when prompted, choose to "Keep on My iPhone" if she wishes to keep that information. If she does not want or need any of this, then skip down to the selection below to delete the iCloud account completely.
Turn iCloud features off
On your iOS device’s Home screen, go to Settings > iCloud, then tap to turn off iCloud features.

When you turn off a feature, you’re asked whether you want your device to keep a copy of your information stored in iCloud for that feature.
Once you have saved the contacts, calendars, etc. that you want from the current iCloud account on your daughter's iPhone, then you can delete the current iCloud account from her device.
Turn off iCloud completely
On your iOS device’s Home screen, go to Settings > iCloud, then at the bottom of the screen, tap Delete Account.
At this point, I would suggest turning off the phone, and restarting it. Then, tap on Settings > Mail, Contacts, Calendars. Tap on Add Account. Tap iCloud. Now type in your daughter's new Apple ID email address and password.
Apple ID: What to do after you change your Apple ID
http://support.apple.com/kb/HT5796?viewlocale=en_US&locale=en_US
Cheers,
- Judy