There is 0 reason a new, young driver needs anything other than a 4cyl. Want and need are two different things.
I happen to think it is important to impart financial smarts as early as possible and a 4cyl gets far better gas milage. If you pay for everything, she won't care and I am sure would LOVE a v8 BMW. Again.. want and need are different.
I came from a family where a car was never a gift. If you wanted one, other than the family car that you had to ask mom and dad to use, you helped pay for it and got a small, reliable car. I taught at a University for a bit in grad school and was utterly sickened by the expensive cars those kids drove. They had 0 understanding of worth, with mommy and daddy footing the bill, and were the worst kind of spoiled. This was a while back, when the economy was rolling strong.
Get her whatever you want, but don't let anyone tell you that you NEED to get a 19 year old anything other than a small 4cyl. Those arguments will be self serving and not practical. If you wish to buy your daughter the car she wants, do it. It is your money, but lets be real honest. Many of us on here grew up with a small, slow car with no power anything and without A/C. I did. I didn't own a car with power windows and AC until after college, and you know what is such a shock to kids today... I SURVIVED!!!!
Get her the 4cyl and save the gas money.