To the OP, I don't think it is such a problem. I would just be glad that she is interested in playing music. Reading music is an enabling skill, in that she will be able to expose herself to a wider range of written material, and also more easily self-teach music theory.
But in the end I think that the single most important thing about learning music is to play and enjoy playing. Also, when your daughter memorizes a piece learned by any method, she internalizes it, just as she would if she originally got the piece into her brain by reading it from a printed page. I think it is actually a better indicator of musical talent, and a better starting skill to have, to internalize a piece of music by simply hearing it than by reading it.
I don't think you will be wasting money on a good piano teacher if your child can't read music by the fall, either. If your teacher gives written lessons, that will likely help to resolve the reading issue quickly, since your daughter will probably memorize the small pieces and compare them with the written notes in front of her as she plays. Plus there are all sorts of non-written things that a good music teacher teaches, including beginning theory, posture, fingering, breathing, etc.
