These all sound lovely! I’d like to put in a vote for obsidian- I got some recently to keep around and it has a really nice, soothing energy for a protective stone. It’s also easy to find and relatively inexpensive, which is nice 
As for quartz, perhaps rose quartz? It’s not a protective stone per say, but it is a good one for someone who is sensitive/an Empath because it helps nurture love, especially self-love. I’ve found it helps the one who wears it to be more gentle, understanding, and compassionate (both to themselves and to others) 
Whichever stone(s) you choose, I hope they are a big help for your daughter! Good luck and blessed be to both of you 