Not much to add to rosfrog's excellent reply, apart from maybe one issue that hasn't been mentioned yet:
The girl's age.
I would actually suggest that a young singer that age should not use a too heavy mechanism in general. I know they all want to, and they all think they can because that's what they hear on a daily basis - but a kid's voice is not an adult voice (a 25-year-old popstar doing it doesn't mean a 12-year-old should), and even adolescent voices should be very careful with attempting a belted sound. I usually don't introduce this if the basics aren't safe.
I know there are people out there who think it is okay for a 12-year-old to belt - but I don't, no matter what everyone else says. I have a few inherited "stageschool-singers", and their voices were close to ruined when they first approached me. I am really quite sensitive on this matter ...
rosfrog's advice will prevent her from attempting to do so if you demonstrate it in the right way - otherwise, she will probably still try to push, no matter on what vowel (although EE is far less risky than AH and EH).
So what you IMHO really need to show her is to use a lighter mechanism than she does at the moment (if I have the right idea about what she does - it is difficult without actually hearing her, but I have my own "usual suspects" in that age group, so I think I get the picture

). Don't let her shout her way up until the voice cracks, she shouldn't attempt that one note in the same mechanism she uses on the lower notes. In fact, it should be exactly the opposite - she already has to use a lighter mechanism much lower than she does at the moment. If that doesn't happen, she won't hit the Eb without cracking in a million years ... It's a bit of a "fake belt", but that's absolutely okay for a kid that age.