Hi there,
There is no need to take any music exams in strict order, from personal experience (many moons ago) I went straight in at Grade 3 on the flute, missing out Grades 1 and 2. I am now a music teacher, and my pupils often skip exams, if they are progressing very quickly, which it sounds like your DD is!
I don't know very much about the Musical Theatre exams, but Trinity/Guildhall and Associated Board (ABRSM) are both very good music examining boards, and they don't need you to take the exams in order. My DD did Grade 1 singing with Associated Board last year (she was 8 at the time) and she got a distinction, though next time I think we might look into the Musical Theatre exams as this is where her passion lies!
I am sure your DD will do very well at Grade 3, her teacher would not have suggested she skip otherwise!! Good luck
