There are 4 public member trees on ancestry which have Michael & parents
3 have his birth year as 1848 but I could not verify either year on rootsireland or www.irishgenealogy.ie/
1 has his mother as Eliza
I did find a baptism record of Michael Williams with mother Catherine (not Ludgate) & father not John in 1844 but the poarish is not Fermoy!
If you google assisted passengers Queensland you get Qld Archives; there are 4 Michael Williams.
If the 1848 birth year is correct, there is a Michael Williams in the list who arrived 6 Aug 1866 aged 20 on the Netherby/City of Melbourne which is close
However, does this mean he arrived in Melbourne?
Queensland BDM has their marriage in 1876; do you have a copy of this as it MAY have his age in 1876.