Found her christening, using the parents' names:
Agnes Gordon, bapt. 6th January 1799 Maybole - parents George G and Janet Kennedy
So it looks like the entry you found for 1851 is correct:
Fullarton Street, Dundonald, AyrshireAgnes Gordon, head, wid., 48, washerwoman, b. Maybole
Janet ", dau., -, 8, -, b. Dundonald
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