While newness is no guarantee of serviceability, you would need to run a chkdsk /r to check for bad sectors on the HDD.
To view its report go Start - type eventvwr and press enter.
When Event Viewer has read the data, expand Windows Logs - click on Application/Action/Find then type chkdsk or wininit into the Find box and then press enter.
Cancel the Find box and then you can read the full report in the scrollable window.
Other than a report on the status of the volume, look to see if there are any KBs in bad sectors.
Microsoft are no longer selling anything Win 7 related so you will have to go for the OEM Recovery disks and that would be my first choice as it will have all of the drivers in it, unlike a Win 7 install disk.
You will need to back up your daughter's personal stuff which is separate from the OS and if she has any paid for programs, ensure you have the product keys for those.
With what you will save on not buying a Win 7 install disk, you could put that towards an external HDD which is better for backing up stuff onto as well as creating system images.
There's one thing to remember though with using an external disk for system images and that it will overwrite previous system images and you have to boot up with a Win 7 Repair disk to use the one I made earlier option.