Is it possible that Magda's name was inadvertnetly omitted from the family in the 1911 census? (a mistake by the census taker) I guess we can't know unless she is found in the census elsewhere.
The word on the Copenhagen police registry is Alder = age = birth date.
You are saying Magda was pregnant when she left Copenhagen for America? When was her child born in USA? Do you have that birth certificate? Is the father named?
She has been living independently in Copenhagen since 1914 and leaves Copenhagen 29 April 1915, traveling to her friend Mrs. L. Greer in Wilmington, North Carolina. Probably she is not being "shipped off," would be my guess. Her father and stepmother could refuse to allow her to return to their home to carry out her pregnancy, but as far as I know they could not compel her to leave Denmark.
On the passenger manifest, when asked by whom was passage paid, she answers: self
Here's that 1906 census you already have - would it help to post the 1911 census for the family as well?:
1906 Danish Census
Svendborg, Sunds, Egense
Laurits Theodor [Skytte] Knudsen born 2/11 64 Gift, Husfader Lærer [Skaarup Sogn - Svendborg Amt]
Ane Kirstine Knudsen [født Rasmussen] 10/4 76? Gift Husmoder - [Egense Sogn - Svendborg Amt]
Ebba Elisa Knudsen 28/3 98 Ugift Barn - [Egense Sogn - Svendborg Amt
Villiam Knudsen 30/4 00 ? Ugift Barn - [Egense Sogn - Svendborg Amt]
Magrete Karoline Knudsen 19/12 00? Ugift do [Barn] - [Egense Sogn - Svendborg Amt]
Rigmor Ingeborg Knudsen 14/12 05 Ugift do [Barn] - [Egense Sogn - Svendborg Amt]
Magda Katrine Knudsen 5/12 89 Ugift do [Barn] - [Egense Sogn - Svendborg Amt]