Annemie is a contracted form of
Annemarie used in Dutch-speaking countries and occasionally in German-speaking countries (although in the latter case it's usually considered a diminutive of
Annemarie).
See:
https://www.linkedin.com/pub/dir/?first=annemie&last=&search=Suchehttp://www.meertens.knaw.nl/nvb/naam/is/annemieand "Duden. Lexikon der Vornamen" (the edition published in 2013)