This depends a great deal on how extensive this database would be. The more personal data was stored in the database, the more objectionable it would be. However, if the database did not have a lot of personal information, it would not be such a big deal.
It is certainly justifiable for the government to want to know who comes into Canada. It needs this information so that it can know whether there are criminals or potential terrorists entering the country. If the government is worried about people entering the country and then staying illegally, it is justified in keeping a database of their immigration statuses and of the places they intend to visit in Canada. Finally, it is worth knowing who comes into the country and how long they stay in case certain people end up having suspicious patterns of coming and going.
Of course, if the database were to try to collect more information, it might tend to infringe on people's privacy. This would be less acceptable because it would have less of a clear connection to security.