I think I may have found your Anna Jensen in Denmark. There was an 'Ane Jensen', age 30, who registered to emigrate to the US on Mar 3 1882. She gave her last residence as Købelev (Lolland), Maribo Amt.
Looking in the parish registers for Købelev I found an Ane Jensen born July 7 1850. Her parents were Jens Ramsus Henriksen and Karen Johanne Pedersen. Looking a bit further in the records (some census some parish records - I didn't look up all the births) I found that she had siblings:
Cecilia Jensen b abt 1845
Carl Henrik b. Aug 5 1846
Karen Marie b. abt 1848
Petrine b. abt 1852
Knud Wilhelm b. abt 1854 (found him on the 1855 census but not the1860 so he may not have survived)
Hans Frederik b. Oct 21 1857
Camille Christine Vilhelmine b abt 1859
Rasmus Adolph b. May 27 1863
Christian Ludvig b Dec 29 1864
The birth dates for her siblings doesn't quite match what you have, but the names are there....
Hope this helps,