Correct spelling for the English word "Quavemire" is [kwˈe͡ɪvma͡ɪ͡ə], [kwˈeɪvmaɪə], [k_w_ˈeɪ_v_m_aɪə] (IPA phonetic alphabet).
There doesn't appear to be any information available on the etymology of the word "Quavemire". It is possible that "Quavemire" may not have a well-known or documented etymology as it does not seem to be a widely recognized or used term.