It's been a while, but I believe Alan Taylor would be your best resource for your question. It is important to note that Canada startes seeing an increased settlement after the Revolutionary War by loyalists and people drawn to attractive settlement incentives. Furthermore, there were settlers from Scotland during this period, again, drawn to some of the incentives for colonizing the largely empty Upper Canada region.

Canada's defense was largely made of conscripted militias (many of whom were probably born in the Thirteen Colonies or Britain), a few soldiers, and large amounts of native Americans.

Taylor, A. The Civil War of 1812: American Citizens, British Subjects, Irish Rebels, & Indian Allies. New York: Vintage Books, 2011.

Edit: changed Lower Canada to Upper Canada.

The only reason I'm replying to this is I stumbled on a War of 1812 website the other day when replying to another thread here. The links I'm providing aren't anything I can verify but they look passably researched and comprehensive. Link #2 has extracts from actual books, with permission from the Canadian War Museum.

Chart of British Regular Regiments

http://www.warof1812.ca/charts/regts_na.htm

Slightly more information on various regiments:

http://www.warof1812.ca/regiments.htm

This isn't answering your question directly but will at least give you information to make an educated percentage guess.