Avoid MACE. Too often it ends up getting into the face of the person deploying it. It won't stop someone who's cracked out, either.
Get her a self defense keychain bauble like a kubotan. Teach her how and where to strike and grab (nose, throat, solar plex, groin, etc).
Discrete, lightweight, useful.
Not a weapon to most.
I'd highly recommend getting her into martial arts. Good for the body, good for the brain.