I think you have the right idea when you say you're going to e-mail her about the option of counselling. Let her know that it's a great thing, and she doesn't have to immediately step in there and scream "I cut!" or self-harm or whatever. Let her know baby steps are the key, and she might find it helpful even if she chooses not to speak about her self harm.

You're a good friend for caring, remind her that you'll always be there for her.