According to the Female Convicts Database (
https://www.femaleconvicts.org.au/ ) Judith's maiden name was Cahir and children Ann, Eliza and James were sent to the Orphan School
http://www.orphanschool.org.au/showorphan.php?orphan_ID=2980http://www.orphanschool.org.au/showorphan.php?orphan_ID=2986http://www.orphanschool.org.au/showorphan.php?orphan_ID=2996also - 1850 birth of William to William Kelly and Judith (Cahir)
https://stors.tas.gov.au/RGD33-1-28-p708j2kEliza was apprenticed as a servant to W N Belcher of Melbourne - looking at the writing in orphan school registers, this was possibly W R Belcher, Clerk of Petty Sessions
http://search.archives.tas.gov.au/default.aspx?detail=1&type=S&id=SWD28http://search.archives.tas.gov.au/default.aspx?detail=1&type=S&id=SWD7In September 1849, Eliza Kelly, ex-Hobart Orphan School, was charged with obtaining goods under false pretences. She had recently been discharged from the service of Mr O'Shanassey.
1849 'LOCAL INTELLIGENCE.', The Melbourne Daily News (Vic. : 1848 - 1851), 23 August, p. 2. , viewed 23 Mar 2018,
http://nla.gov.au/nla.news-article226473207The name Eliza Kelly features in more police reports after this, but its hard to say if these are her or not. Another Eliza Kelly, imprisoned 1869 and 1872, had arrived from Liverpool per Greyhound in 1863, and an 1870 death of a habitual drinker named Eliza/Elizabeth Kelly was a married woman.
Eliza's father, William, departed for Melbourne in 1852, possibly for the goldfields.
https://stors.tas.gov.au/POL220-1-2 pg66
It would be interesting to find out if the family reunited somehow