Q: I am looking for the birth record and ancestors of: Margaret FITZSIMMONS, believed to have been born in London, Middlesex, Ontario, Canada ca 1847. Her father FITZSIMMONS was born ca 1813 in Ireland. (First name unknown) Her mother was Harriet Eliza BARNES was born 1818 on the Isle of Wight, England. She emigrated to the US sometime before 1864, where she married Michael DOUGHERTY in Manhattan, New York, US, 1864.
A: The family arrived in New York on the ship Gideon arriving March 22, 1848 . The family group was Thomas Fitzsimmons 33, Harriet Fitzsimmons 29, Harriet Fitzsimmons 7, and Margaret Fitzsimmons age 2. They are found in Ancestry's
New York Passenger Lists, 1820-1957
I had a look in the census records for USA for 1850, and the family is there in New York specifically New York Ward 1
The family consist of Thomas FITZSIMMONS, 43 born Ireland; Harriet FITZSIMMONS, 31 born England; Harriet FITZSIMMONS 10 born England and Margaret FITZSIMMONS 5 born New York. So your Margaret was not born in Ontario, and although this census says she was born New York, her arrival on the ship Gideon in 1848 indicates otherwise.
You might want to view the image for yourself, and search other census years. See All Census Records for help with census
I also found the family in the 1860 census for New York Ward 1 District 1, New York, New York. Little Harriet is now missing and Thomas FITZSIMMONS age 10 has joined the family.