iMessages being delivered to both me and my daughter
Yes, you'd need to get her a different Apple ID for iMessages to be sent separately. You can do this by one of two ways:

Method 1: Create an Apple ID using Gmail, Outlook, etc:

If you want to create an Apple ID, but don't want to have to restore the phone to do it, visit the Apple ID management page. Note: your daughter will need an existing email address to do this. Follow the onscreen instructions to create the new ID using the existing email.

Method 2: Create an Apple ID by restoring the phone:

If you want an email address ending in @icloud.com, then you have to reset the phone by navigating to General &gt; Reset &gt; Reset all Content and Settings and confirming the prompts onscreen. Then, when your phone resets, you will be able to create an Apple ID during the setup process.

Otherwise...

Otherwise iMessage will view as both of you as the same person.

The reason iTunes assigned the phone number to the iPad because, again, it thinks you're the same person because both devices are linked to the same Apple ID.