The first thing you can do, assuming you are paying the bill anyway, is to keep her on your insurance instead of getting her own policy. You have probably built a more stable driving history, and that can offset the cost of insurance for a new driver. Until your daughter has had a chance to develop a safe driving history of her own, or reaches the age of 25, she would be well advised to stay on your insurance for as long as she lives at home.
Another way to keep the cost of insurance down for your daughter is to keep her grades up. Most car insurance companies will offer discounts to students who maintain a 3.0 or better grade point average. Showing the world that she is a responsible person lowers the risk she represents for the car insurance company.
If your daughter is satisfied with driving an older car, you can save money on insurance for the car. You can also lower insurance costs by increasing safety features, such as having a theft prevention system, or anti-lock brakes. The rated safety of the vehicle will have a large impact on the insurance rates you are offered.
Instead of getting your daughter her own car, you might want to consider adding her to your policy but allowing her to share the family car. This reduces the amount of time she could possibly be on the road, and that mitigates some of the risk associated with new drivers. Some new drivers begin this way and then get into their own car after showing a responsible attitude towards driving, a move that could save you a lot more than just money on your insurance policy.