I was musing – as one does – about how to put "Personal Ordinariate of Our Lady of the Southern Cross" into Latin; and I recalled that St Mary of the Cross is not called in that language Sancta Maria Crucis, but Sancta Maria a Cruce.
Hence, on the analogy of the UK's Personal Ordinariate of Our Lady of Walsingham, Ordinariatus Personalis Dominæ nostræ Walsinghamensis, it seems to me that the Latin title for the Australian Ordinariate should therefore be Ordinariatus Personalis Dominæ nostræ a Cruce Australi (perhaps without capitalizing "Southern Cross").
Please correct me if I am wrong!
Also, I recall that, while in the Diocese of Toowoomba – the only part of Australia having Our Lady of the Southern Cross as Patroness – her feast is kept on the 1st of September, even the latest Australian edition of the modern Missal contains no notice of this, no proper Mass, nothing. Will the Australian Ordinariate also feast Our Lady a cruce australi on the 1st?