I haven't seen Dong Yi, but I think it did have the same director as Dae Jang Geum, and possibly a lot of the same actors.

Isn't the little Jang Geum adorable? This was the first K-Drama I ever watched, and I just fell in love with that little girl. I wanted the whole drama to be about her as a child. But then when Lee Young Ae appeared as the adult Jang Geum, it got even better. Just the best character I've seen in any drama.