OK, so that wasn't great, but it was off the top of my head, and to be fair I've never written fan fiction for Harry Potter. But, I had fun. I sat in my car and wrote a few sentences in somebody else's world, and it was satisfying and creative. My brain engaged, spinning tales, and looking for connections from J. K. Rowling's world to my character, Rose. There's not a lot required for fan fiction if you don't want there to be. Take a planet name, take a school, take the bare minimum necessary to get your juices flowing. Or you can borrow heavily from the world already created and set up your adventure. It's all up to the writer.
As a reader, I already know the basis for where my characters are and what they may or may not do. For example, I know that Rose cannot apparate. She's too young, and it's not allowed on Hogwarts grounds. I also know that her having a cat at school, is both allowed and encouraged. I know these things because I've read the original Harry Potter's. Without that knowledge, there may not have been enough world building already there for me to understand and know about implicitly. This frees both the writer and the reader to have to pay attention to less. They can focus on using words to express their story and less of the background. All of that hard work the author already did.