The information I have gleaned from various Australian records suggests you do in fact have mixed up more than one EBERHARDT family.
“”3 Carl Theodore EBERHARDT (1870 - 1938) b: 1870 in Campbell Town, Tasmania, Australia, d: 1938 in Launceston, Tasmania, Australia””
TROVE digitized newspapers has an Obituary for this man. http://trove.nla.gov.au/ndp/del/article/52215559?searchTerm="Eberhard"&searchLimits=l-decade=193http://trove.nla.gov.au/ndp/del/article/52215559?searchTerm="Eberhard"&searchLimits=l-decade=193 The death of Mr. Carl T. Eberhard yesterday removed one of Launceston's most prominent business men and a public spirited citizen. Mr. Eberhard, who was aged 76, became ill only last Wednesday. Born at Yandoit, Victoria. Mr. Eberhard lived at Clunes and Ballarat for some years. . . . . . From the VIC index. Pioneer Index. Victoria 1836-1888 Carl Theodor EBERHARD Event: B Father: Ernst Mother: Catherina HEUSER Birth Place: YAND Year: 1863 Reg Number: 5476
Naturalization records can be viewed online for Phillipina Eberhardt BUTLER and George Philip EBERHARDT. http://www.naa.gov.au/collection/using/search/http://www.naa.gov.au/collection/using/search/ In 1912, Phillipina stated she was born 16 May 1845 in Nassau, and had been in Tasmania for 55yrs. In 1916, George Philip stated he was born 29 Oct 1851 in Nassau, and had been in Tasmania for 60 years.
TAS Archives have records of the arrival of these EBERHARDTs on the ship Montmorency in 1855. http://portal.archives.tas.gov.au/menu.aspx?search=8http://portal.archives.tas.gov.au/menu.aspx?search=8 Eberhardt Cathage 9 Eberhardt Catherineage 34 Eberhardt Gottliebage 3 Eberhardt Heinriskage 38 Eberhardt Johanage 33 Eberhardt Mariaage 50 Eberhardt Peterage 24
The Colonial Tasmanian Family Links database does not have registered BMDs but has these listed as follows. Johan = John Philip Catherine = Katherine Elizabeth wife of John Philip, were the parents of Maria Catherina born 1857. Cath aged 9 on the passenger list is most likely Phillipina. Gottlieb = George Philip Maria = Maryc1804-1863 Heinrich = ?Henry 1825