Let's go into this a little further: do you know anything about the Moore side of the family?
The reason I ask is that "Alkana" is another form of the name "Elkanah". And there is an Elkanah Moore, b. 1811 in KY living in Knoxville, Knox Co., IL in 1880. He married Nancy A. Elder on 18 Apr 1844 in Knox Co., IL. Their children were old enough to be the parents to your Alkana. Many people were lost in the Civil War and through disease before the 1880 Census.
On the Allen side, there is an H. C. Allen, b. 1835; Ireland, living in Summit, Knox Co., IL, married to Eliza J. ?, also b. in Ireland in 1845. They have a daughter, Margaret, b. 1864; IL, that could be your Margaret. She also has six siblings, which means you might find out something through her family.
Does this sound possible? Perhaps a start for this snowy Christmas in Illinois.