It is iTunes crashing. Does it happen every time? If so, go to Finder, click the GO menu in the Menu Bar, hold down the Option/Alt key, click Library, then in the new Finder window go to the folder called Preferences, open it and find the file called com.apple.iTunes.plist and delete it. It is preferences file, it does not delete any data, only settings. Try opening iTunes again.
Sometimes that can help.
Sorry, but as you only posted a report for iTunes and did not mention other applications crashing and did not provide further information, we cannot simply guess what is happening.
Tell your daughter to back her data up and let her know how to reinstall Mac OS X via clean install or just normally without deleting stuff but repairing it.
She could always try the PLIST delete procedure before doing a restore.
The PLIST files always have the name of the application in their name.
Another option would be to try a different user account, even if newly created. If that does work, the issue is account related.
But since there is an intermediary, you, it is hard to troubleshoot. Maybe make her register here and post in this thread to let us help her?