I tip my hat to Fr. Stephen Smuts, who has published the new coat of arms of the Australian Ordinariate of Our Lady of the Southern Cross.
The artwork is by Sandy Turnbull and the well known church heraldist Fr. Guy Selvester acted as a consultant.
The shield includes the four stars of the southern cross on a blue background known from the Australian flag plus the crowned “M” to symbolise Our Lady.
The only question I have concerns any particular significance of the eight-pointed stars, since the stars on the flag are only seven-pointed. I have found an interpretation of it as a universal symbol of unity. It is said often to be used by native peoples.
The blue is also slightly brighter than the dark blue of the flag.
… and then they were three
ORDINARIATE NEWS (from the Anglicanorum Coetibus Society) 
The eight-pointed star is the Ballarat Star (not to be confused with the newspaper), so called because of its use on the Eureka Flag which flew at the Eureka Stockade in Ballarat, Victoria. While many meanings have been applied to it, I would tend to see it as a symbol of self-determination in this regard, while the Southern Cross as a whole acts as a symbol of guidance.