I think Raithnineach is a version of Raithneach - bracken or fern
bracken oh little woman? (perhaps asking for kindling for fire to make the potato bread (steampaí)? Raithineach could also refer to a place name derived from the plant name.

the other version of the chorus, Rachaimid a bhean bheag, would mean "let's go, oh little woman"

There are several versions of the song, different verses.

Another recording to look out for is Seán Corcoran (group "Cran")