I'm related to John MILLER who married an Amelia Dallas BAYLY in Waitati on 21 June 1877. I got a copy of their marriage certificate from Knox College but at that time parents weren't recorded on certificates so can't confirm her parents.
I've downloaded two family trees from the internet, one giving the information you posted and another showing Amelia Dallas Bayly born in 1855 in Eddlestone, Peebleshire, Scotland in 1855. Her parents being William Henry BAYLY and Janet MURRAY.
I just checked the NZ birth registration indexes and found an entry in 1858 for an Amelia BAYLY in New Plymouth, folio # 57, which is probably your Amelia.
Are you able to throw any more light on whether it is your Amelia Dallas BAYLY or the Scottish one who married John MILLER? Do you know how your Amelia may have come to have an Otago connection?