When a man was transported to Australia his family was left without means of support.  It was common for his wife and children to end up on parish relief or in the local workhouse.

“ … In petitions seeking mitigation, personal circumstances were frequently cited to demonstrate factors like the convict’s good character, their innocence, that they were seduced into crime by others, or driven by desperate circumstances; perhaps they were too old, sick, young or insane to be sent overseas or remain in prison. A commonly made plea is that the convict’s transportation will leave their families destitute: without their income, the convict’s family, be they elderly parents or a young wife and children, will be forced on to parish relief.

But faced with the misery of separation from their loved ones, and potential destitution from the loss of their income, we also find many petitions from those seeking to join family members in New South Wales or Van Diemen’s Land. Most of these petitions are from wives, many of them wishing to travel with their children to join their husbands in exile, although there are also examples of convicts requesting that if they have to be transported their families be allowed to accompany them.” 

http://blog.nationalarchives.gov.uk/blog/share-fate-petitioning-join-transported-overseas/#more-26696

An Extract from Chapter 1 of:  A Voyage to Establish a Colony at Port Philip in Bass's Strait On the South Coast of New South Wales, in His Majesty's Ship Calcutta, in the Years 1802-3-4  by James Hingston Tuckey (1776-1816)

“… Among the convicts on board, were some who, by prodigality, and its attendant vices, had degraded themselves from a respectable rank in society, and were indebted to the lenity of their prosecutors alone for an escape from the last sentence of the law. Some of these men were accompanied by their wives, who had married them in the sunshine of prosperity, when the world smiled deceitfully, and their path of life appeared strewed with unfading flowers; in the season of adversity, they would not be separated, but reposed their heads upon the same thorny pillow; and as they had shared with them the cup of joy, they refused not that of sorrow. Those alone who know the miserable and degraded situation of a transported felon, can appreciate the degree of connubial love, that could induce these women to accompany their guilty husbands in their exile.

 The laws can only make distinction in crimes, while the criminals, whatever may have been their former situation in life, must suffer alike for crimes of the same nature: it therefore entirely depended on us to ameliorate their condition, and grant such indulgences, as the nature and degree of the crime, and the otherwise general character and conduct of the prisoner seemed to deserve. To these helpless females, all the attentions that humanity dictated, and that the nature of our service would admit, were extended, but still it was impossible to separate their situations entirely from their guilty husbands, they were consequently far, very far, from being comfortable; and one of them, borne down by the first hardships of the voyage, which she felt with redoubled force from being far advanced in her pregnancy, fell a victim to her misplaced affection before our arrival at Teneriffe.”  http://adc.library.usyd.edu.au/data-2/tucacco.pdf

Thomas Peters and his wife Mary Ann (Ann) had a daughter, Elizabeth, who was born on 25th August 1801. (She was baptised on 7th October 1801.) When Elizabeth Peters was just 20 months old, she and her parents  set sail for Australia aboard the prison ship Calcutta.