This is what I have for you!
Nils's family is originally from Vang, Oppland, Norway. The area is called Valdres.
They left Vang April 8th 1854 and the original name is not Gilbertson, but Guldbrandsson. The farm was Tvedt.
http://digitalarkivet.no/cgi-win/webcens.exe?slag=visbase&am...As you can see, they came over with three kids (Anders became Andrew, and Guldbrand became Gilbert in the USA). And the name of Anne was Andersdatter, women in Norway kept their maiden names when they married, because it showed who their father was. Anne's father was Anders.
1860 Census - USA: Adress: Bergen, McLeod, Minesota,
Nils Gilbertson: 48
Annie A. Gilbertson: 45
Andrew N. Gilbertson: 18
Gilbert Gilbertson: 15
Nils N. Gilbertson: 12
Baton (Betsy) N.Gilbertson: 10
Annie M. Gilbertson: 4
1870 Census - USA: Address: Bergen, McLeod Co., Minnesota
Another kid: Maria
Hope this was of help :)
Anne Karin