It's one of these names with uncertain origins, but it seems to most likely be derived from Brud, the name of several Pictish kings. It definitely predates the use of surnames, and in its modern form has been recorded as a forename since c1750, so yes, I'd say it's pretty traditional!
Im scottish and I think l Brodie is the boy's spelling and Brody is the girls spelling from what and who I know. Im not 100% sure how factual that is but the 2 Brodie boys I know are spelt that way and the 1 girl Brody I know is spelt this way. Hope this helps!! Its a lovely name. The Red King I think its meaning is. It so happens two of the Brodies i know have red hair!!