Can you provide a few more details, please? Such as when she was transported, where from, any family names? I have a whole line of the Ball family, and Elizabeth was a favourite name, but I don't recall any of them being transported to Australia...
An Elizabeth Ball was transported to Van Diemen's Land in 1819."Arrived per ship "Friendship". Ship's Master: Armet; Current Status: Convict; On Stores: Off; Residence: Hobart [TAS AUS]; Tried at Newcastle-upon-Tyne [NBL ENG], 1815, Trial Sentence: 7 years [Biog Item No. 200115529]" Source Tasmanian Muster 1819, transcribed from State Records of New South Wales by Garry Wilson. See: http://www.bda-online.org.au/mybda/search/biographical-report/20011552901?f=Elizabeth&l=Ball&ol=&i=3&s=&p= (You may have to be a member to see this link.)