Maybe some perspective will help. I would have given anything if my daughter had been able to get her license at 16. She has some physical challenges, and after a lot of hard work and countless hours on the road got her license at 18.5. There are many parents who wish they had your "problem"! Be proud that your daughter has reached this important milestone along with her peers.
I understand that some people are more scared of some things than others. I am not nervous when my daughter drives, but when she recently flew alone for the first time, I was a wreck. My little girl, walking through an airport alone! (Notice that I'm the only one who thinks of her as a "little girl"; everyone else sees a young woman returning from a job as a camp counselor.)
Having a driver has been a lifesaver for me! I am having trouble handling the heat (it's in the hundred teens now here) and she does almost all the driving. I can send her to the store. (Teens LOVE to drive anywhere.) She can drive herself to work, and this year she will drive herself to school. What a break for me!
So enjoy your own private chauffeur. Relax and read a book or chat on the phone while she does the work. Or send her out to do boring and annoying errands while you do things that are more important or fun. This can be a great new chapter in both of your lives!