To start you on your way, here's the 1871 Canada census entry for Alice Smith with her parents, Henry and Phebe in Rawdon, Hastings County (family starts on line 17):
http://www.rootschat.com/links/0gnw/It took some time but I found them on the 1861 Canada census with names that were definitely spelled phonetically by the enumarator (I'll spell them as they appear so you will have an easier time finding them if you are able to search the census yourself):
Henery Smith, farmer, born Upper Canada, Baptist, 56
Pheby Smith, born Upper Canada, Baptist, 49
Polly Smith, born Upper Canada, Baptist, 23
Robert Smith, labourer, born Upper Canada, Baptist, 20
Daniel Smith, school master, born Upper Canada, Baptist, 18
Emely Smith, born Upper Canada, Baptist, 14
Henery Smith, born Upper Canada, Baptist, 12
Silas Smith, born Upper Canada, Baptist, 10
Allis Smith, born Upper Canada, Baptist, 5
I haven't been able to find the family on the 1852 Canada census.
There is a Henry Smith who died in Rawdon, Hastings County on 10 Aug 1883. He was 79 when he died. It also indicates he was a farmer, Baptist and born in Canada. Henry is listed as a widow on the 1881 census. I couldn't find a death for Phebe so either she died before registration started in 1869 or her death wasn't registered.
Jacquie