My mother is a little bit overprotective when it comes to driving, help?

Hello! I turned fifteen some amount of months ago, and that is the legal age in my state to get a permit. But my Mother thinks drivers are too dangerous down where we live, central Florida, and says I'm not even allowed to get my permit until I am eighteen. The thing is, Florida has the rule where you need a permit for a year and THEN you can get your license.

My Mother complains and gets extremely annoyed/frustrated whenever I ask her to bring me somewhere (My best friends house, fifteen minutes away.) I understand gas is a major money consumer, but she rarely drives, only to work which is a minute away. She just complains she's exhausted all of the time, and makes me feel bad when I ask.), then she acts like she has to bring me and snaps at me during the entire car ride, and I always ask her politely.

I've tried telling her I'm a responsible driver (I have driven on golf carts, an electric, various types. Some that go as fast as the average speed limit in my city.) and she still refuses, by saying others are not responsible enough.

I would buy my own car and gas, (I saved my money from baby sitting.) because that's my responsibility, but I am home schooled, so I'm kind of lonely without anybody to talk to, or when I'm not able to go out to the local park or something. I just feel like a car would be a good thing for me. She doesn't.

Any ideas on what I should do? Thanks.