Jesus. The kid is eleven years old. If you pressure your kid too much im sure she will quit due to lack of fun. And dont forget that she will become a teenager soon, and if she doesnt like what she's doing then, i can almost guarantee you she will quit.
The best way of learning something is by having fun with it. Sure, you need to work hard but its very important to have fun at the same time. At eleven your not able to control your form of whatever. There will be up and downs, everybody has. I dont see the point of having a super coach for a eleven year old. I promise you that high level players or 'regular coaches' at the club can teach her how to play. In my opinion you can start going after the big coaches when the people around just cant help you anymore.
Just because people like McIlroy and Djokovic by many did succeed at a very young age, doesn't mean that everybody can, and you can still be successful even if your not world no. 1.