This family are proving to be quite tricky: we are reasonably sure that John's father was the William Andrew "of Nancekuke" who was buried on 24 August 1828, at Illogan, and his age at burial is given as 48 (born 1780). We have found young John (a blacksmith), and his sister Mary Ann, at Porthtowan Common, in the household of a Martin Rickard and family in the 1841 census, and it's possible the Rickards are relatives, as a William Andrew and Grace Rickard married on 25 April 1816, in Illogan. (If this is the right couple then Martyn, bapt 1817, was their firstborn.) We also know there were at least five other Andrew couples baptising children in Illogan at the same time as William and Grace, but haven't yet been able to establish if they were related.
We can't raise hide or hair of brothers Martyn and George, or their mother Grace, in the 1841 census returns and, in addition, there are deaths registered in the Redruth district for a George Andrew in Dec Q, 1844, and a Martin Andrew in Mar Q, 1848. John left for Australia not long after his marriage in 1848, so there's no help there, either!
I have trawled through the Cornwall OPC, FreeReg, FamilySearch and anywhere else I could think of in an effort to find more of the family but have so far drawn a blank. I have, though, found burials in the 1860s for a William and a Grace Andrew in St. Stithians parish, who may be the parents of the other John you found, baptised in St. Stithians in 1817.