If you're a little car savvy you can get her something older. I mean, there are tons of 70's and 80's sedans in good shape for cheap. That's what I did for my first car. Paid $200 for a 74 Cutlass Supreme, then spent about $600 on new carpet, tires, seatcovers, etc. Then about 3k miles later my father and I did a rebuild kit on the olds 307 for about $400.
So for under $1500 I got a car that lasted all through high school.
I will say that I didn't have to deal with the current gas prices, so that may be a consideration. I took care of that ride because it had my own work in it. I think that is a key thing to do for a new driver. Make them pay for some of the car (I understand that making your daughter work on it may be a stretch) then make her maintain the insurance so she can see the impact that speeding/accidents have on your wallet. I have 4 sisters, and out of them only one got a free car. She got 3 speeding tickets and abused it to the point of my father and I rebuilding the engine twice. Make her contribute as much as she can.