AskOliveTree response: Carole, I hope you have gathered all the census records available for your family. Since Ontario and England took their census every 10 years in the same year starting with 1841, you should be able to find William in 1841 England, then 1851, 1861, 1871, 1881, 1891 and 1901 in Ontario.
William Johnson, born 1821 in Lancashire, England; died 1908 in Varna, Ontario. Occupation, carpenter. [He married] Mary McQuarrie
Johnson, born 1825 in Ireland; died 1912, in Varna.William Johnson's parents were Thomas Johnson and Jane Martin Johnson Mary McQuarrie's parents were Andrew McQuarrie and Mary (maiden name unknown)I have no further information concerning my Johnson and McQuarrie forebears. Any help you might be able to provide will be greatly appreciated, including dates of migration to Canada and the ships on which they migrated.
I use Ancestry.com but you can also find some Canadian census records on Automated Genealogy, FamilySearch and National Archives of Canada
I've suggested these years and locations based on the 1861 census for Stanley Township in Huron County where I found the family with their oldest child age 13 born in Canada. We know from this record that William and Mary were married and living in Ontario by circa 1848.
Questions Asked on Census Records
Each of those records will provide you with clues to further research such as occupation, religion and so on. The 1901 census for example asks for a year of immigration to the country and this will narrow your timeline for William's arrival.
For a list of what questions were asked on each of those census years, see AllCensusRecords.com
Agricultural Census Records - Don't Overlook These!
An important and often over-looked resource of the 1851, 1861 and 1871 census in Ontario is the Agricultural Census. This shows the exact land location of an individual, how many acres he had, how many were cultivated, what he grew on the land and so on.
For help with the Agricultural census you may want to refer to my blog posts on Finding Ancestors on 1851 Agricultural Census Canada and Ancestry Goof with 1861 Canadian Census
I suggest searching the Agricultural Census for three reasons - first you will learn more details about your ancestor if you find him, and that means you're getting a better sense of the person other than names and dates. Secondly finding his exact land location (Lot and Concession Number) means you can branch out to searching the Abstract Indexes to Deeds, the Township Papers and more.
Land Records Are Useful
Each of these records has different information. The Abstract Indexes for example will give you dates for when your ancestor first purchased his land and when he was last living on it (sold or transferred it to another individual) Sometimes you will find references to other family members, or even a will.
The last reason is that your William is listed as a farmer in 1861, 1881, and 1891. I'm not sure why you gave his occupation as "carpenter" in your email to me but perhaps he showed that occupation on a census I didn't check? It is a pretty big occupation discrepancy though so I'm a bit puzzled by it.
Farmers usually owned their own land so he is almost certain to be found on the Agricultural Census records.
Ships Passenger Lists & Immigration Records
From the 1901 census we are told that William immigrated in 1845 while Mary says she immigrated in 1843. Since Canada did not require that ships passenger lists be kept before 1865, this will be a challenge for you to find records of their passage. Surviving lists are few and far between. What has survived are other records such as immigration agent records, shipping company records, steamship records of travel down the St. Lawrence River from Ports of Arrival in Canada - and those records are what you will need to search in.
Some of these alternate ship records are online and links to all known substitute records, offline and online, can be found at Filling in the Gaps on Olive Tree Genealogy website. This is where your search for their immigration should start.