Here are some other threads on this subject from the past:
http://forums.animesuki.com/tags.php?tag=girls
I second
Kemono no Sou-ja Erin though I recommend
pre-screening through episode seven before deciding if it's appropriate, preferably with your aunt or uncle as well. I suggest involving her parents in any recommendations you might give her.
I'll also recommend
Dennou Coil. All the kids are your cousin's age peers. As it's unlicensed, though, it does raise the issue of whether you want to introduce this young girl to watching illegal material. I'd also consider how her parents would feel about this.