Wayne I checked the film 2138 at our local LDS library - Agents Immigration List - ' Ascendant' left Plymouth 2 Mar 1858 and arrived Moreton Bay 19 Jun 1858. Assisted immigrants,
Wilkins, William aged 28, labourer from Cambridge, C of E. neither read or write. / wife Mary, 28 from Surrey same, Emma 3, dau from Cambridge and son Isaih 1 from Cambridge. Then checked the Qld indexes and didn't find anything on Emma. There was a record for a birth for John, b 11 Jun 1850 [ think this is an error and should be 1859]ref 1859/001490 and he d 16 Jun 1859. Parents listed as William Wilkins and Mary Titmarsh.
Mary Wilkins [Titmarsh] d 17 Jan 1860 with parents as John Titmarsh and Uniey Simpson ref 1860/000140. If you obtain her death certificate it would list all of their children, living and deceased. Couldn't find any record of her birth but found her parents marriage as John Titmarsh and Eunice Simpson, 15 Oct 1828 at Croydon Cum Clapton, Cambridge. [ lds film no 0990297 - item 4] The following were baptisms of their children on the same film, Rebecca 17 Sep 1843; Isaiah 16 Aug 1840 ; William 25 Feb 1838. John 31 May 1846 on film no 1040456. There is a church member's entry for Jane bc 1829 and d 10 Jun 1915. The 1881 census and baptism, marriage records for some of your family are on the LDS family search site. LDS libraries also have free access to the scanned images of census records from 1841 - 1901. For instance William and Lydia Wilkins are still alive on the 1881 census at Arrington. You will be able to find the male Wilkins eg. Rule Wilkins at Kingston Cambridge with wife Harriet and son George. Their marriage is available on lds film no 1040535 at Kingston, Cambridge. Her name was Harriet Chapman. Found a Rule and Harriet Wilkins on the 1900 census of Westchester, Mount Pleasant, New York and it states that they emigrated in 1884. Don't know if their yours. The baptism records for the children of William Wilkins and Lydia Rule are available on lds film no 1040363 for Arrington. The 1881c states that Lydia Wilkins [ Rule] was bc 1805 at Wimpole, Cam. [ parents were William and Elizabeth]