Yep, perfect example.
The problem with that is you aren't on Twitter yet. When you go to join Twitter, there may already be an @Laurie31, or you may decide on a totally new name, like @Laurie3100 or DisGirlAllie may want to be called @TwitterGirlAllie. So when your niece is improperly using it, she might be accidentally using someone else's Twitter name or referring to you by a name that you don't/won't have.
I don't know a lot about Twitter, but as far as I know, an appropriate use of the @(screenname) on another site or correspondence is when quoting someone from Twitter. Like when we post a news or web article, we include the corresponding
link. To refer to a Twitter Tweet, one would say, "@(screenname) just Tweeted this joke or picture. . ." Then people would know to go to Twitter and enter @(screenname) to find that person's corresponding Twitter page. The @(screenname) IS the link to their Twitter page.
Your niece is referring to you as @Laurie31, when you don't even have a page.