Why 'abjured' rather than just 'resigned'? To abjure means to solemnly renounce, recant or repudiate, none of which can really apply to a job. The words 'My' and 'Friday should, of course, have capital letters and perhaps 'co-worker' and 'going-away' should be hyphenated.
it's not exactly wrong, and it does make sense, but 'abjure' is a very literary word that sounds out of place in ordinary speech about jobs. As QM suggests, 'resigned her position', or just 'resigned', would feel more normal. But if you're deliberately trying for a quirky effect, yes, it would be ok.