Newbie needs help

I got some help and found my relatives, the Liens, shipped out on the Cunard "Dampsk Hero" to Liverpool. If this listing shows Cunard, does that mean the first Cunard ship is the one they took to America? Also, how long was the Norway --> Liverpool trip? In other words, how much lag should I leave? http://digitalarkivet.uib.no/cgi-win/webcens.exe?slag=visbase&filnamn=EMITROND&variabel=0&postnr=39512&fulle=true&spraak=e Any hints on how to determine which ship they embarked on?