I don't know many kids who
want to do homework. Most of us do so begrudgingly if at all.
Yes, it is (in most cases... some teachers just assign busy work) beneficial to do homework. However, I don't recommend forcing her to do it. The best motivation is self-motivation. Take a step back. Don't pretend not to care - you should care. Just realize that DD is in high school, now, and it's time to loosen the reigns a little bit. She might feel the need to rebel because she feels as if nothing has changed at this supposed turning point in her life.
Where does DD do her homework? You might've had her sit down at the kitchen table after school each day to complete her homework after middle school... if so, it's time for a desk. Now, my sister and I have desks in a loft, which is great because if we need help, we can call downstairs or consult eachother (but annoying because dear father feels the need to flip on the television as soon as he gets home). Consider moving her work area to a family room or her bedroom.... or just letting her choose where she works (my sister likes to sprawl out on the floor... I prefer to sit upright).
Now, I know it's hard, but.....
Don't ask what her homework is. Don't ask if she has any projects or when her tests are. Don't offer any school reminders. Let her keep up with her own assignments. If the school doesn't provide her with an agenda, purchase one for her. This is the time to build organization and study skills. And how it's done depends on the individual.
Okay, now don't worry - she's going to (most likely) fill you in (most likely when she's complaining about her difficult teenage life! xD). You just have to establish a relationship so that you aren't her reminder mommy, anymore - you're the mother of an "independent" young adult.
I have a feeling that since your daughter is excelling in school, she may not be doing her homework because she finds it unnecessary. She'll eventually realize that although homework is boring, it's (in most cases) necessary for success.