Problem 1: This sounds silly, but, were empire dresses called the same thing back then? For reference, I'm thinking about something like Folkwear pattern #215.
Problem 2: An eight-year-old girl from an aristocratic Scottish family is being sent away from home (not to boarding school, but to tutoring. This does work in the fantasy context). What kind of clothes would her family send with her? Descriptions, or even pictures would be greatly appreciated.
For problem 1 I tried various permutations of "empire dress" and "empire dress 1810s" through Google and Wikipedia. For problem 2, I'm really not sure what to search for. Tried permutations of "nineteenth century children's clothes", which got nothing useful.