The 1851 Canadian census covered Canada East, Canada West, New Brunswick and Nova Scotia. The National Archives of Canada has now announced that the 1851 census has been scanned and placed online. It is available at no charge at the National Archives' web site.
The online site allows researchers to search by geographic location only. As this is not a nominally-indexed database, it is not searchable by family name. The digital images within this database are copies of the original microfilm records held by Library and Archives Canada.
1851 Census images for New Brunswick and Nova Scotia are presented with the support of the Provincial Archives of New Brunswick (http://archives.gnb.ca/Archives/Default.aspx?L=EN) and the Nova Scotia Archives and Records Management (http://www.gov.ns.ca/nsarm).
You can read more and access the online census records at http://www.collectionscanada.ca/archivianet/1851/index-e.html.
My thanks to Wanda Sinclair for telling me about this new resource.