At long last I got the information I needed from the National Archives (dreadful service).
Patrick Doyle sailed on the Royal Charter from Liverpool to Melbourne, leaving port in early May 1859. He was undoubtedly my great great grandfather as his age and place of birth match the other records I have.
The documents TNA sent me show that this was his first, and only, voyage, as he was drowned during the return voyage in the notorious storm off Anglesey in October when he was nearly home, having left Melbourne on August 18th.
He was employed as a Fireman, which I believe means he was what we now refer to as a Stoker, on a wage of £4.10.0d per month. As he was away for more than 5 months I am puzzled about his final wage - £12.9.6d
Many thanks to everyone for their help with this search.