Female equivalent of "fellow"

Solution 1:

According to Etymology Online, fellow has been:

Used familiarly since mid-15c. for "man, male person," but not etymologically masculine.

It would be perfectly acceptable to call a woman a fellow traveler, for instance.

A similarly toned word for a woman, but not related to fellow, might be simply lady, or woman, as in, "my dear lady...".

Solution 2:

Fellow in the context of an organization or group is gender neutral. Girl, woman or gal otherwise.

Solution 3:

I think you could conceivably get away with using "fellow" for a woman. ("For she's a jolly good fellow!", although that may be limited to the context of the song.) If you want a word with the same sort of archaic feel as fellow, "chapess" might do the job, although it's both colloquial, and a neologism, as was as being more obviously paired with "chap".