And there are plenty of people who are unhappy because their parents pushed them into a career that they do not enjoy. Hell, most people in IT seem to fall into this camp along with a lot of doctors and lawyers. Think about what is important to your duaghter's life and life in general.
The best outcome for someone is letting them be happy and content. It is not your life (you the parent) it is your daughter's life and you should encourage and support her to be whatever she wants to be. You get to set the moral framework and create a mentally and physically healthy environment but she is not your play thing that should do your bidding.