The procedure you suggest will work in most cases, but as Hagar de l'Est indicates, some formatting choices give strange results when converted.
Download and install Word Viewer from Microsoft (free download for MS Windows) to ensure that documents made in Writer will turn out OK in Word.
Unless the project at hand is in a course specifically teaching that software product, requiring Microsoft Office 2007 format may even be against the law (depending on where the school is located). If you can spare the time and want to pursue the issue, the links in the thread Hagar points to make for very interesting reading. In particular when you have the following background info: (according to what I've heard from reputable sources) MS Office 2007 files do not comply to the ISO certified OOXML format, and that ISO certification has been disputed for quite a while.
However, it will probably not help your daughter if you try to force the issue, at least as long as converting at the library is a workable solution. Be pragmatic about it, but by all means give the school a signal that you don't appreciate this forcing of "standards". In the long run it may help your daughter as well as other students (and teachers).
Apache OO 3.4.1/4.1.2/4.1.3, on Ms Windows 7/10 and Mac OS-X 10.8.5 and 10.11.
LibreOffice 4.3.3.2 on Mepis Antix MX 14