Hi John
I am also looking into the Hazlett family as my mothers maiden name is Hezlett which has been spelt as Hazlett/Heazlett/Hayzlett over the years. my GGF was James Samuel Black He(a)zlett and his father Samuel H(e)azlett appears to have immigrated to Australian in 1864 aboard the Sandringham with Alice Heazlett. Interestingly Alice was sponsored by Edward Horrigan (husband of Ellen) - I assume this is a misspelling of your surname. Samuel H(e)azlett died in 1910 and listed on his death certificate are his parents, Robert and Alice. So I am assuming we are distantly related!
Another point is the fact that one of the Hezlett's married into a Wilson in Australia - although this may be a coincidence.
Cheers Peter