Gun is a much better idea, or even pepper spray. It takes skills to effectively fight with a knife.

Knife fighting is up close and personal and it's a very nasty business. First and foremost, in my opinion you had better be a good fighter to begin with before thinking of using a knife, because remember, most likely you will have to "fight your way to your knife" before you can use it. Knives are very poor defensive weapons for those not trained to use them.

Talk her into getting a reliable handgun that is easy to operate (small revolver), something like a Lady Smith, or any lightweight .38, and then take her out and teach her how to use it properly. Better yet, after teaching her to use it, get her signed up in some handgun classes with someone who teaches people professionally. Encourage her to practice as much as she can.

Most of all, try to teach her the importance of carrying herself with confidence and not looking like an easy victim. When it comes to human predators this can be one of the best ways to keep yourself out of harms way. Bad guys don't want to mess with someone who looks like they'll fight back when there are plenty of others who look frail and meek.