Oh, wait. From the "plot bunny" comment:

Firstly, for purposes of this idea, the reason magical training starts when it does (whether the canon age of eleven, or some later date, like thirteen or sixteen), is because that's when most wizards and witches can control their magic well enough to get consistent results from a wand. Late bloomers might be mistaken for squibs (if the parents or guardians don't go bug Dumbledore to check the Hogwarts Book), while early bloomers often experiment with wandless magic, as young Tom Riddle did (see Book 6). Hermione is probably an early bloomer, magically speaking, in the setting of this idea:

[snip]

Hermione shyly-but-unashamedly explains that she was running an experiment, and it went a little wrong. The idea ended at that point, but kept repeating with minor variations. Her parents might have been two of the three people who died. She may or may not be sociopathic or evil enough for keeping her collared to be the best thing for all concerned. It rather depends on whether or not you want to do a 'tear down the wizarding world' story from this.