Does anyone know what sort, if any, records were kept in the 1840's for individuals immigrating from Canada into the U.S.A.?

I am trying to locate a family that came to the United States sometime between 1841 and 1843 (1842 is mentooned on one child's later census record). I don't know what part of Canada they moved from, but I do know they went to Illinois.

At the time, the family should have consisted of the following:

-John Lindsay
b: UNKNOWN DATE in Scotland
-Sarah Lindsay
b: about 1811 in Ireland

-Matilda Lindsay
b: about 1834 in Canada
-David Lindsay
b: June 1836 in Canada
-John Lindsay
b: about 1838 in Canada
-Mary A Lindsay
b: about 1836 in Canada (could be between 1836-1841)

I'm not sure if the last name was always spelled Lindsay, but it is always seen spelled that way, so it is probably safe to assume this spelling, although Linsay, Lindsey, Linsey or any other variation wouldn't be surpirzing.

If anyone knows of these people or who I could contact to get information on their crossing the Canada-U.S. border, please let me know. I am haveing a horrible time finding information on this family in both Canada and the U.S. and am hoping someone might be able to help me shed some light on the whole subject. Thanks everyone.