Hi, several things you can do. First, I would get a copy of his death cert from October 1848 and his marriage cert from 1841 as both may have information about his parents. Also, William was naturalised on 1st June 1843 and you could obtain a copy of his naturalization cert which usually has good info on it. Lastly, if you go onto the scotlandspeople website (its a pay per view but is inexpensive), and go to OPR births put his name in and birth span 1800-1809 county Ayr there is 1 record which should be him. In the 1841 Scotland census, there is a John Collins with his wife Elizabeth & children of Craigie who are most likely related.If you then go to 1851,there are quite a few Collins' in Ayrshire some of whom look like they could be brothers & sisters to William. On scotlands people once you have William & Margaret's marriage cert, you can confirm if the Margaret Campbell on the ship "Francis" with William travelling with her parents is indeed the same one he marries.
Hope this helps,Kim