According to the online tree, Pernille married Abraham Corneliusen Eide in Crawford county, Wisconsin, on 17 Mar 1881.
They had 15 children. Pernille died 13 May 1928 in Miner county, South Dakota. All 15 children were born in South Dakota.
In America Pernille apparently used the last name "Williams". If you go to this free site, you can see the births of their children:http://apps.sd.gov/applications/PH14Over100BirthRec/index.as...
Just enter the last name "Eide". Then look at the ones born in Miner county.