It was so easy.
I simply placed the name of her father, David Williams, in the search box of TROVE, the family history portal of the National Library of Australia.
The first entry on the list of digitalised newspapers was the arrival of David and Alice and their five children - Margaret, David Jnr, Ann, John and James - in Sydney on the ship Mary Catharine on Monday 21 October 1833 was the first on the list.
The Sydney Herald, Thursday 24 October 1833
SHIPPING INTELLIGENCE. ARRIVALS.
From Liverpool via Hobart Town, on Monday last, having sailed from the former port on the 15th June, and the latter the 9th instant, the ship Mary Catharine, 391 tons, Captain Benjamin Rock Jones, with sundries. Passengers ... Mr David Williams, cooper, Margaret, Ann, John, Jane, Alice, and David Williams ...
Among their 76 fellow passengers were merchants, milliners, cabinet makers, farmer, carpenters, painters, coopers, pastry-cooks, a harness-maker, a clerk, a surgeon, a teacher and an attorney, plus 10 members of the ship's captain's family.
A 'cooper' was a man who made and repaired wooden barrels used as storage containers.