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Here is what we have found about the name "Emer".
According to O'Corrain & Maguire (a standard source for Irish names) (1), Emer is the wife of Cu Chulainn. If a name is only known to have been used by a legendary character, it's unlikely to have been used by real people. Therefore "Emer" is unfortunately not probable as the name of a 12-13th century Irishwoman.
Sincerely,
Hartmann Rogge
Academy of S. Gabriel
(1) O'Corrain, Donnchadh and Fidelma Maguire, Irish Names, The Lilliput Press, Dublin 1990.