I'm sorry to hear you don't trust her enough, but that doesn't mean there can't be a future. Maybe time will tell whether you think she is ready or not.
I know the desire to tell those you are close to or love, and honestly I have only done so on very few occassions. Sometimes it has ended badly, sometimes it has been ignored, and rarely have I found anyone who accepts it and tries to understand.
If the two of you are happy, just enjoy each other and see where it leads. As suggested before, maybe try and educate her subtly, and work out a way to prepare her if you truly want to tell her.
In the end the decision is yours though, and what you think is best.