Any occupation listed for her father? Any idea what religion she was?
Have you eliminated John Cairns (44, born Ireland) & wife Margaret (age 42, born Dalry, Ayrshire) with daughter Mary (age 12, born Glasgow) living in Glasgow in 1901? I know this Mary is born 10 years before 1899 but sometimes birth years aren't accurate- especially if husband is younger.
May could be a nickname for Margaret, Mary, Maud, etc. and spelling of surname could vary.