I see that when Thomas and Elizabeth married in Ontario in 1860, Thomas was residing in Oshawa and Elizabeth in Whitby.
Therefore, this looks to be a likely bet for them on the 1861 census of Canada (image available on Ancestry.ca). East Whitby, Ontario, Canada West (roll C-1058-1059, p 4):
Charles Kirby, Labourer, b. England, W[esleyan] M[ethodist], age 55, married
Mary A. Kirby, b. England, WM, 51, married
John H. Kirby, Painter, b. England, WM, 29, married
Huldy Kirby, b. U[pper] Canada, WM, 25, married
George Kirby, b. U Canada, WM, 2
Thomas Kirby, Painter, b. U Canada, married during the year, WM, 23, married
Elizabeth F. Kirby, b. England, married during the year, WM, 25, married
Charles Kirby, Weaver, b. U Canada, WM, 18
Joseph Kirby, Weaver, b. U Canada, WM, 16
William Kirby, b. U Canada, WM, 14
Daniel Kirby, b. U Canada, WM, 11
And then on the 1851 census of Canada: Whitby, Ontario, Canada West (roll C_11742, p 41):
Chas. Kirby, ..., b. England, No Religion, age 44, married
Mary Kirby, b. England, No Religion, 40, married
Nancy Lacant, b. England, No Religion, residence Uxbridge, 23, married
Jane Kirby, b. England, No Religion, 16, single
Thos. Kirby, Labourer, b. U[pper] C[anada], No Religion, 14, single
Chas. Kirby, b. UC, No Religion, 10, single
Joseph Kirby, b. UC, No Religion, 9, single
Wm. Kirby, b. UC, No Religion, 6, single
Daniel Kirby, b. UC, No Religion, 2, single
Susanna Lancount, b. UC, No Religion, residence Uxbridge, 2, single
Chas. Lacount, b. UC, No Religion, residence Uxbridge, 1, single
You can see in 1851 and 1861 it says he was born in Upper Canada, which included much of southern Ontario. Quebec was in Lower Canada, so that may just be a mistake on the 1871 census.
A search of Bill Martin's Wesleyan Methodist baptism index shows several Kirbys, including Thomas's next youngest brother:
bap. 27 Jan 1842 at Gananoque, Leeds Twp., Johnstown: Charles Kirbey, s. of Charles & Mary Ann, b. 26 Jan 1842 at Gananoque.
So this places the family in Gananoque in 1842. On a quick search I have been unable to locate a birth or baptism record for Thomas.
It appears Charles had a military background – it may be him in lists of the 4th Batallion Incorporated Militia. This may be why they ended up in Canada. There are many avenues of research to pursue here, and it will help you better determine where the family was in 1838. Start by taking a look at
Canada, British Army and Canadian Militia Muster Rolls and Pay Lists, 1795-1850.
The next step would be tracing when and why the family immigrated from England to Canada. It must have been just before Thomas's birth – about 1837 – since his sister Jane was apparently born in England.
It is relatively straightforward to trace Charles and Mary back in England, but that's beyond the scope of this question. Investigate the various marriages and deaths of Thomas's siblings – many of them include Mary's maiden name. You need to fill in some other gaps first, but when you get to that point I'll suggest you start your search Allerthorpe, Yorkshire, England.