ANSWER - Whether or not you choose to allow your daughter a knife is entirely up to you as a parent and should you choose not to then your daughter can be confident that lack of a knife will not impede the work she wishes to undertake as a witch. But what I will do is set your mind at rest in relation to the purpose of a witch's knife so you can make a fully informed decision for your daughter.
The witch's knife is usually referred to as an athame and your daughter is correct that the knife is used in ceremony. The principle function of the athame is to direct energy, will and intent. A witch may use her knife as a tool to draw the circle inside which many witches choose to work. This circle may be designated sacred space (particularly in Wicca) or may mark out protected space where a witch can work safely without influence from spirits.
It would be incorrect to say that no witches use their knives for practical purposes (which can include sacrifice though in modern witchcraft this is rare) as for some witches, especially those who would term themselves "kitchen witches" the knife can have multiple functions including mundane tasks like chopping herbs or carving symbols into candles. If your daughter is inclined toward Wiccan witchcraft then the knife is far more likely to be kept separate from day to day life and used exclusively for magic ritual. It is a Wiccan belief that no blood may touch the athame and a Wiccan witch is extremely unlikely to involve herself in any form of blood sacrifice. (Wicca is far more widely practised than any other form of witchcraft particularly among young people so I would be willing to bet this is the path that has caught your daughter's interest.)
I think it is great that you are so open to discussing your daughter's path with her and she is lucky to have a mother with a genuine interest who wants to understand rather than judge. Should you choose not to permit an athame please tell your daughter from me that crystals, wooden wands and even sparklers (!) can be put to use for much the same purpose as an athame and she mustn't feel that lack of a knife will hold her back from what she wants to achieve.