Lunella really does come up with the best gadgets. The fact that they're makeshift stuff made out of random junk makes them so awesome.
Not that unrealistic, actually. A school administration that simply doesn't understand how to handle a child of her intelligence, parents who likewise have trouble with her, and a desire by parents and administration both for Lunella to socialize with kids her own age. I'll bet you could find a ton of geniuses out there who had experiences like that in school.
Once she's older, she might start skipping grades.