I've recently discovered a webcomic that sort of has a supergirl in it. Though all she can really do is fly.
Heres the first entry on its about page.
Lighter than Heir is a story about a young girl named Zeppelin Von Schultheiss. She's the daughter of her country's greatest war hero, Hemmel Von Schultheiss. All of her life, she was surrounded by love from the public and the media due to his accomplishments, but it never was enough for her.
She was always stuck in her father's shadow, never appreciated for her own accomplishments. With resentment for her father and a huge ego, she signs up for the military on her 19th birthday in hopes to outshine her dad. But a sheltered life filled with fans doesn't doesn't exactly prepare her to face a world with people who don't like her!
I've read up to the current page tonight and I'm going to be following this for sometime now. Maybe some people here will enjoy it as well