Hi Mike
There appears to be at least one more child, Thomas William - birth Mar Qtr 1859.
It would make sense, especially with Scottish parents, to name the next son born after little William died 1856, the same name - in this case as middle name.
FreeBMD, for ref:
MARRIAGE of parents: Sep Qtr 1855 - William McARA and Ann BROWNLEE
BIRTH William - Dec Qtr 1855
DEATH William - Dec Qtr 1856
BIRTH Ann - Mar Qtr 1857
BIRTH Thomas William - Mar Qtr 1859
BIRTH Margaret - Mar Qtr 1861 (so is possibly no more than 5 or 6 mths old at very most in Census 1861 )
Census 1861: 16 Upper Burrage Place, Plumstead, KentRG9 / Piece: 408 / Folio: 65 / Page: 40
Head: William CAREY 30, Blacksmith, b Scotland
Wife: Ann CAREY 33, b Scotland
Dau: Ann CAREY 4, Scholar, b Plumstead
Son: Thomas CAREY 2, b Plumstead
Dau: Margaret CAREY 4 mths, b Plumstead
Sad to see, then that little Thomas William also appears to have died, at about age 5.
DEATH: Sep Qtr 1864 - Thomas William McARA - Lewisham
Was hoping the 1861 might have had a more specific POB for the parents

. William died 1879, is that right?
But the occupation Blacksmith could be important, as it may have been passed down father to son.
It would be interesting to know what brought him down to that part of Kent (near Woolwich); I'm wondering, if there may be an Army connection - especially with he being a Smith . The marriage Cert may be the best next step to advancement.
Cheers
AMBLY