I have a mystery too which may or may not connect. My grandmother told me her mother Mary Cecelia Grealy b. Dublin 1880 was given the choice of two trips when she graduated from school in 1899. She could visit either her Australian or her American cousins. She chose America but I have wondered what the Australian connection may have been.
Her parents were John Joseph Grealy b. about 1853 in Galway, possibly Athenry, and Mary Hughes b. about 1847, location unknown.