There's really nothing to go on here. Ideally, the story should be about her development in some way. Do you have any ideas for the story itself, or do you just have a character in mind at this point?
No I have written out a small outline. - girl about 17 - name: Elizabeth - family of wizards - both parents wizards even though they technically work in the human world they got to keep their powers because both jobs are used in the wizard world - Mom works in the human world as a photographer - still photos and moving (again spell has to be shown for moving pics) - Dad works as a human book store but if you're a wizard and show the cashier a secret spell you can go to the back where they sell wizard books - has a younger brother - also a wizard - been taught wizardry since a young age by parents - goes to high school with humans - now trying to figure out if she wants to live in the human world and go to college or to love as a wizard and go take an apprenticeship - live above the book/photography studio - Elizabeth helps out in both - likes the bookstore better
Shouldn't she be a witch? Characters from all genres usually undergo a similar development. As long as she is human, she has human psychology. She will have flaws, perks, shortcomings, talents, emotions, behaviours, etc. Whether your story is fantasy or not should not serve as a factor in your character's development. She can be dynamic (change throughout the story) or static (does not undergo any changes throughout the story). She can be flat or round. She can be interesting or stock. It's really up to what you want to do with her.
I don't know much about your fantasy world, but if there's any kind of creature that's a threat to people, or other type of feared predator, then your wizard could kill it even though previously she didn't have the ability to. Of course, you should avoid Mary Sue-esque scenarios where she magically defeats something like that with zero prior experience (like a boss!). But maybe she has to dig deep and face her fear, and it makes her more capable and mature. Kind of like Hermione Granger and the troll in the bathroom.
What is the conflict of your story? There's no plot here, and that is cricual for character development. So far you have nothing but set up - you don't even really have a character, as you've said nothing about her personality, just facts about her family and home situation. What does your character want? What is important to her? What's standing in the way of her achieving it?
What you've done is filled out a character sheet. "What is good development?" Well, let's define development first: Growing to become more than what they began as. That basically means that there's a before and after, several "after"s if you're doing it right given that the transition usually takes a while. With that in mind, a snapshot isn't worth very much. A character doesn't develop without a story of some kind - Kallithrix is right in mentioning this. It's oversimplistic to simply give a laundry list of basic details and expect the community to develop your character for you. Think of some random situations - ACTUAL random situations, ones that aren't already tailored to your character. There are innumerable online sites that can give you prompts for this kind of thing. How your character responds to these situations determines you character. The lasting effect of several scenarios in sequence on your character is how you develop them. Good luck.
