Katherine Halverson - Immigration to Australia

I am searching for information in relation to my great, great grandmother. Her name was Katherine (or Kate) Halverson, who was born in Norway. I have no details regarding the ship that she took, or the dates. The only information I have is that she settled in Mackay, Queensland, Australia. She married an Englishman, William Webberly in 1887 in Mackay, and they had 6 children. Is there a site that I can search, by the passenger's last name, in order to find out the ship's name and arrival in Australia? I would also like to find out more about her family history in Norway - can you recommend any sites?