An old post but maybe it's okay to add a little anyway. It's a really good question that applies to a lot of Danish immigrants.
Here's the Danish emigration record mentioned:
Navn: Jensen, Jens Chr.
Stilling: Husmand (occupation)
Bestemmelsessted: Deloraine, Can.
Kontrakt nr.: 98100
Fødested: ? (birthplace)
Sidste oph.sogn: Vrejlev Sidste (last residence)
oph. amt: Hjørring
Sidste oph.sted: Vrejlev, Hj. A.
Bestemmelses land: Canada
Bestemmelses by: Deloraine
Bestemmelses stat: Manitoba
This registry was kept in Copenhagen and so the port of departure was Copenhagen.
Here is a description of emigration from Gothenburg, Copenhagen, and Oslo in the late 1800s:http://webcache.googleusercontent.com/search?q=cache:NGVPiMz...
From Copenhagen the family most likely took a ship to Hull, England. From Hull, they likely took a train to Liverpool. It was common for Danish emigrants to take a "feeder" ship and then a train to get to the large port of Liverpool. Typically we don't find records of these interim passages.
The family departed Liverpool as previously noted aboard the Scotsman. The Scotsman was probably the S/S Scotsman of the Dominion shipping line. (BTW here is a story about the sinking of the Scotsman the following year as it journeyed to Quebec):http://www.norwayheritage.com/articles/templates/great-disas...
As noted this family arrived Quebec 28 May 1898.
By 1898 Quebec was well equipped with options for traveling further west. Travelers could journey west by train or by ship. A network of canals and locks had been built to ease the journey by water. Lots has been written about these transportation options. Most often no records are available online to document a specific family journey.
The information about the quarantine island is very interesting! :D