Looks like a good basic set.
I might be more inclined to start her off in Acrylics first. They don't require as much patience and they dry fast which means you won't have to find "paint drying" space.
I'd also look into some local workshops like art the art museum or Michaels and places like that hold little weekend classes for all skill levels. It's fun and good exposure.
Best of luck to her. My daugter is an artist as well. It's been amazing watching her grow into her craft.
Agreed... acrylics over oil any day for a beginner. Oil, which is much more advanced IMO, being more difficult might turn her off to painting entirely. If its something you want her to come to love, start small and easy and teach her basic brush and color technique and application with acrylic. Once she starts to "master" it tell her there's much more she can do with other mediums, such as oil. Good luck and have fun!