Library and Archives Canada has a database, linked from here, with 33,036 references to immigrants who stayed, were born/baptised, married or buried at the Grosse Île Quarantine Station between 1832 and 1937.
The records are particularly valuable for those of Irish origin for the period before 1865 after which passenger lists for incoming vessels to Quebec City/Montreal became available.
The database has transcribed all information contained in the various source documents. While it is possible to obtain copies of some of the original records, those in the custody of the Québec Service Centre of Parks Canada contained in oversized registers are too fragile to consult, or even for photocopying.
That’s unfortunate as the search capability at LAC is limited. You can search by surname, given name(s), and keyword. If you know the name of a ship of interest you can search for that in the keyword but results displayed don’t show the year. You have to click the item number for each hit to see that. It would be useful to have a tabulation of the ships by year, but you cannot keyword search by year.
You could get lucky and find information on a ship and voyage, but hardly any passenger names, at The Ships List.