I am the danish cousin, Maj-Britt.
I wish I could show you the 1911 census for Magdas parents and siblings, but I can't access the information as I have problems with JAVA, and now I really wish i had written down the opslagsnr. Sorry.
I can tell you that the whole family except for Magda are there, I have looked at it several times before my computer problems, there is nothing in the tillægsliste either.
I have looked through about 75 % of Svendborg Amt 1911 census', and nothing yet. Hopefully my JAVA problems are temporary and I can continue my search.
About the shipping of, this is just the story that my grandmother was told, by her mother. In this story/skrøne Magda was about 18 years old when it happened, and of course we now know that she left for America when she was in her mid twenties.
You write that I am guessing, and yes I am trying to guess where she went, what she did and where to look for her, as I have next to no clues.
I have found old letters she sent, and is looking for any information that might give me a clue. In one letter she writes about Vor Frue Kirke in Copenhagen, and how she walked past it many times, maybe that's a clue. But not being able to access census', all this information did was that it made me frustrated.
Sorry that I'm not able to give you anything more concrete to work with.