No, the Queen quite literally enjoys legal immunity. She's above the law. That is, if she'd play hardball. If she would, to take your example, drive drunk and kill a bunch of kids, she'd probably step down and face some sort of punishment. But she definitely can afford to stay in power and ignore any calls to step down. I don't need to explain that it's an open question to what extent her rulership will still be bearable after that, but meh.
In 1990 a more liberal abortion law was passed over here (Belgium). The king, although having no actual power, has to sign every law. But former king Baldwin refused to sign the law, saying that he couldn't morally do so as a Christian. What they did then is declare the king to be 'unfit to rule' for a day, sign the law themselves in parliament, then reinstated the king. That way the law was passed and he didn't have to worry about his morals.
Just to say: the supra-legal status of kings and queens in most European countries is quite real. And in Britain the Queen is a LOT more powerful than our king, so yes, she probably could get away with most offenses. Even murder. They'd find someone else to take the fall.
Good thing you put the disclaimer at the end, hehe.
An uncle of mine knows the local 'king's prosecutor' (that's the title, translated 
), who has to validate every arrest, fine or whatever that's written out by the police or court(s) in his district. So when he gets caught speeding, he just tells the cops to call the prosecutor and tell him his name. They almost always apologize and let him drive on, heh. Gotta love a little corruption.