I think it works out at about once a fortnight for our JAs.
I would not be too worried about height, and I can never really tell what the Royal Ballet school are looking for (or at!!) we had two girls in the same year offered second auditions for White Lodge Ballet School who were completely different! One was tiny in frame and the other taller, and quite muscular.
Our dance school currently have 3 JA girls, all of whom are quite skinny girls. It's not just about build though, and they will look at feet, ankles and what they can comfortably do with regards to flexibility and turn out. We had one girl, who after a year of doing JAs, did not make it into the MA program. They said she had particularly short tendons and her body had basically reached its limits. Her mother was devastated! That said she is still dancing, and could quite possibly have a very successful career If she so wishes in the future, possibly in musical theatre or contemporary dance.
Not all JAs go on to be ballerinas. In fact most of them don't I would have thought! I know several ex JA girls who have given up dancing completely as they found other interests and I know several who are now, at 16-20 yrs old at dance colleges. I also know one who has gone on to White Lodge. However, she has ALWAYS been very focused and known what she wanted and even she has struggled with the intensity of the expectations of her at the school.
Could your dd do a "JA for a Day" workshop? I know in the past they have run these workshops for prospective JAs to see if they like the regime, and it may give you more p an idea of how your dd would fit in. It is quite prestigious for some to be a JA. Also, if your feel at the moment she isn't ready for it then she could always audition next year. It's not a ":do it at 8 or miss out" they can audition (or re-audition) for each year of the program. I know children who have been unsuccessful for two or three years and then got into the program in the third year.