No, you can safely decide to ignore the friend request. The request will be shown as pending when they view your profile. But, since the request is already pending, they will not be able to send you another friend request.
However, you can decide to decline the friend request if you are sure that you would not wish to be in their friend list. Doing so will not let them know that you have declined the request, but they will be able to send you another request.
Thus Facebook does not explicitly notify the member concerned about the friend request being deleted. But it is quite easy to figure it out. So I would conclude that your friend will definitely get to know that you have deleted her request.
Live....and Let Live!