I see barely any Equestria Girls covers on Youtube! Or maybe they're just hard to search because there's no real consensus on any of the song names.

The only other Strange New World cover I found was this really pretty one by Mary Medley http://www.youtube.com/watch?v=9W4kDAwbzO4

Thanks to LovelyFluttershy for the instrumental: http://www.youtube.com/watch?v=uu0XoosS6X0