I appreciate your query and don't know if I can help you or not.
Your Albert Moore is not a direct ancestor of mine or even likely a sibling of my gg grandfather Elwood F. Moore. I found an 1850 census record for Elwood as a child of John Moore and Nancy Foreman with a bunch of his siblings, but no Albert.
John Moore was born in Ireland in about 1798. Family tradition says he came over with two brothers, one went north (Michigan?) and the other stayed in Ohio. But you know about family traditions. Next to worthless as far as I'm concerned. Still, they're possibly a clue. I haven't found either of John's brothers and perhaps your line is from one of these????
Have you tried finding your Albert in the 1850 Census? I'll give you a hint. I could not find Elwood, or his father John, in the 1850 Census Index of Ohio. Fortunately, I had a clue that they may have been in Scipio, Meigs County, Ohio in 1850. So I had to find them by going through the entire Census record of Scipio, Meigs Co. page by page until I found Elwood as a child, then I figured out who his parents are. Not an easy task, but it was worth it. I then found a marriage record for John and Nancy Foreman in Harrison Co., Ohio in 1823. So these are possibly some places you might try looking, assuming your Moores are related to mine.
I hope it won't be as hard for you as it was for me. Please let me know if you find Albert's parents. I'd love to find out if his father was also from Ireland and born around the same time-frame. My email address is firstname.lastname@example.org .