Can I change Apple IDs?
You can sort of do this.

You can't make a new account for your daughter and then move existing purchases to be owned by your her new account.  You can use those purchases on her iPod though.

If she already has her own computer account and itunes install just move over to a new iTunes account and make new purchases there.  Change your password and move on.   She will no longer be able to buy with your account. You may need to log in every so often so she can get updates of the apps that were purchased by your account but otherwise things will work fine.

If you have to split her a new iTunes account out of your existing account it's a bit more complex.  There are a number of ways you can pull this off; here's how I would pull this off.


Make a computer account for your daughter. 
Make a new Apple account for your daughter.  
Change your password.
Authorize this new iTunes with your ID.  It's under Store->Authorize This Computer...  This lets her use content you've purchased with out logging in as you.
Use Home Sharing to move your old purchases to the new iTunes.  
Sync her iPhone over to this new iCloud account.


At this point you can remove the purchases for her from your account.  They are in her account and will install and play on her iPhone.  She doesn't have for password and those apps you've already purchased for her are still owned by you.  They won't update without your password.   You'll have to log in for her every so often so that things can update. It'll prompt both on the phone and on the computer when it needs it.