chithead, in case you aren't familiar with birth registrations (you may have William Jr's dob from a death record or family records?) this is where to search:
http://freebmd.rootsweb.com/cgi/search.plUnfortunately there were 1 William Symons whose birth was registered in the last quarter of 1842, in St Thomas registration district in Devon, and 3 William Symons-s whose births were registered in the first quarter of 1843 in Devon: in Barnstaple, Honiton and St Thomas registration districts. (A birth in late December would commonly have been registered early in the new year - but it's also possible that a birth that early wasn't registered.) They may not have actually been from Devon; almost all the other William Symons births registered in the two quarters in question were in Cornwall (with one in London). If he wasn't known to have the middle name Henry as three of the Cornwall births did, that would narrow it down some.
The 1851 census shows one WS the right age with parents William and Jane: born and living in Camborne, Cornwall -- which is in Redruth reg dist, making him likely the birth registered in Dec quarter 1842 in that place.
However, that household had a number of children:
William, 35, Sawyer (wrong occupation)
Jane, 39
Tryphena, 13, at home assistant
Absolom, 11, errand boy
Willliam, 8, wedge driver to father
Eliza, 5
Mary Jane, 3
Caroline, 10 months
- all born in Camborne
... No, that household is in the 1861 census as Simons, still in Camborne. So at least you can rule out the 1842 birth in Redruth reg dist.

It could help find them in the 1851 census if you could confirm whether the couple had other children with them when they emigrated, and if you have any information about them. I'm not spotting another likely household in that census.
There's also the posibility that Jane was a second wife and William remarried between the 1851 census and the emigration in 1855.