It's not bad for a first attempt at fanfiction...unfortunately, it's not your first attempt. The storytelling is stilted, you're describing events and disjointedly at that rather than telling a story, and it's so short, I'd call it a drabble, except it's not apparently intended to be one.

It would make an excellent first draft, a story outline to be built upon and polished into a real story. But it was posted as a finished story, and it's not.

The story concept itself is great, I'd love to read more of it, but the storytelling itself is so painful to read, I just cringe, which means as much as I like the idea, I probably won't read more of it.

I do have a feeling that members of the League will be stopping by when they learn of Lauras arrival.

Actually this is set in the Teen Titans toon universe.