Anne:
Welcome to Ireland Reaching Out!
More than likely they left from Queenstown but I'm not aware of a data base that we have the ship departure information. Have you looked at ships coming into Australia?
I looked for the baptismal records for the two older children born in Ireland. I found these two records Are these the records for the older children? If so, the third child would have been born 1866 or later.
Roger McDonnell
Area - KERRY (RC) , Parish/Church/Congregation - TUOSIST
Baptism of CORNELIUS SHEA of COORCREEN on 25 May 1865
NameCORNELIUS SHEADate of Birth25 May 1865 (BASED ON OTHER DATE INFORMATION)AddressCOORCREENFatherCORNELIUS SHEAMotherMARY SHEA
Area - KERRY (RC) , Parish/Church/Congregation - TUOSIST
Baptism of MARY SHEA of COORCREEN on 10 May 1862
NameMARY SHEADate of Birth10 May 1862 (BASED ON OTHER DATE INFORMATION)AddressCOORCREENFatherCORNELIUS SHEAMotherMARY SHEA