To whom are you comparing your daughter? That would be other 11 year-old girls with no more than 6 months training in some other martial art. You are convinced, hands-down, that she would lose against them all? That is an indictment of her school.
The truth is, there are a lot of schools teaching to a low level of quality. You will get no argument from me over that point. But that is a problem with the school itself and not necessarily the method as a whole. I have always understood that most schools teaching to the younger kids, especially those below age eight or so, are largely a daycare operation with a karate theme. Often they play games designed to keep the kids physically moving and simply having fun. But there is very little actual martial content happening in many cases. This has become more clear to me as I have an eight year-old who will not let me teach him because I am his dad, so I have begun looking at the schools in my area to see if there is anyone I would be willing to allow to teach him. Really, I just want him to be more active and interact with other kids more, make sure he doesn’t become too much of an introvert (I am an introvert myself and am perfectly fine with it, but it is important to make an effort to get out and interact now and again). But I am seeing first-hand how low the bar is often set when teaching these young kids.
At any rate, I don’t believe your daughter is the best example of what training is best for defense or fighting or whatever, because of her age and brief training time and the overall low bar that is typically set in schools that teach lots of kids. And whatever example you might want to use, make sure you are comparing with an appropriate peer group. If the nearest comparison to your daughter is a 16 year-old boy who has been training Muay Thai for a year, I would say definitively she will lose. But that isn’t really a fair comparison.