I have said it before, but I believe that if she survives whe would become a relatively well known writer in the Netherlands (and possibly Flanders), but unlikely outside it. Anne Frank always wanted to be a writer and she was a very good writer (or else her teenage diary would not have been read as much). If she survives the war, she would want to persue a career as writer, probably in the Netherlands, since that is the language she has mastered (that is why I believe she will remain in the Netherlands and not move to Israel or the USA). Since she is a Dutch writer, she will probably not be read outside of the Netherlands (I doubt anyone here who isn't Dutch or Flmish would be able to name another Dutch writer).
Mind you, this is probably the most relevant she can become. It is probably more likely she'll end up as an unknown housewife. Which is not a bad life for a girl in the 40's, but not particularly interesting for this site.