Xeno E03 does sound like a good choice. Has a low mode which is long lasting, AA batteries, medium or high modes if necessary. For backpacking, a warm tint would be a good option for use outside. You could also get it in a red body, so it will be easy for her to find if it gets dropped on the trail. Including the diffusion wand would make it a good campsite light, and still be well within your budget.