When you do an update iTunes archives the backup before the update. If you then sync after the update it creates a new backup. But you should be able to restore the pre-update backup by connecting the phone, clicking on its name in iTunes, and click Restore Backup. When the backup name appears click on it and you should get a list of other available backups; choose the one before the Restore. The only way a backup would be overwritten is if you synced the phone after doing the Restore. Also, if she had set up automatic backup to iCloud you can still restore from there.
Your daughter should be really unhappy with HERSELF for not copying her photos periodically to her computer like you would with any digital camera. See: iOS: Import personal photos and videos from iOS devices to your computer. This is really basic with any device. Apple gives you multiple ways to back up content; if she didn't use any of them perhaps she has learned something. See, for example: Choosing an iOS backup method (Should I use iTunes or iCloud to back up my iOS device?)
In addition, if she had enabled Photo Stream her photos would have been copied to iCloud and her computer in near real time, right after they were taken.
As a last resort, there are many apps available for your computer that can extract content from an iTunes backup. Google "itunes backup extractor".
