Bingo!
101095 1864 vol 16 p 519 Mary Smyth
Mary was born to my great-great-grandfather Hugh Smyth and his wife Jane Booth. Hugh and Jane emigrated from Ireland to Canada and left this child behind with relatives. The first relative was Jane's brother David. Maybe something happened to David and Mary got shifted over to Hugh's (uncle?) James Smyth.
I had seen the birth record online for Mary, but I thought that she had died before her parents left Ireland. That must have been really hard to leave a 4 year old girl behind, in order to move on to a better life in Canada.