Emge doesn't seem to be a very common name in Germany - a search in telephone directories showed that it is concentrated in Lower Frankonia (the river Main region).
125 years ago - information should be found quite easy, since there were (good working) registry offices all over Germany in those days.
If she left from a German port, emigration data are stored at the
German Emigrants Database.
If you know the place she came from (or the region), I could do some researches from here, too.