Hi Harriet . . .
Welcome to Ireland Reaching Out . . .
Your query is complex . . . and covers such a lack of. . . large areas . . of dates and places . . .
Our professional Volunteers would have looked at your data . . . and would have found insufficient information to help in your search . . and most likely passed on to the next Message Board inquiry . . .
Hopefully . . . Yet . . . a local volunteer to the Laois(e) . . ( a.k.a Queens County ) . . area might weigh in . . with additional info . . .
I am not local to that County . . . . but . . . this is what I have to offer . . . .
There is little or no . . recorded . . . records going back to the early 1800's . . . with the exception of . . . a Tax Roll
Tithes Applotment ( 1823 - 1837 ) . . . . when I search it . . for BURKE ( Queens Co. ) . . there are 30 names and locations showing . . .
( see below ) . . . Burke . . can also be spelled . . Bourke . . and other varietions . . .
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Next . . there is another Tax Roll . . . named " Griffiths Valuation " ( 1848 - 1867 )
https://www.failteromhat.com/post1845.php
Again this shows you a general spread . . across Queens Co. . . of the name Burke . . .
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The next records we have . . . is a jump up to the National Census of 1901 . . . giving 100 names of Burke
http://www.census.nationalarchives.ie/search/results.jsp?searchMoreVisi…
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SO . . . I'm afraid . . . it's not of much help . . . attempting to find " a needle in a haystack " search . . .
But . . if you do come up with additional . . useful information infill . . feel free . . . https://www.irishgenealogy.ie/en/
Best of good luck with your search . . on the ground . . .
Cheers . . . E.M.H.