Immigration is already "constitutionalized" and has been since 1867... it is one of the few areas of jurisdiction that specifically designated as concurrent and not  assigned exclusively to Parliament or a provincial legislature.

Per the Constitution Act, 1867:

"Agriculture and Immigration

Concurrent Powers of Legislation respecting Agriculture, etc.

95. In each Province the Legislature may make Laws in relation to Agriculture in the Province, and to Immigration into the Province; and it is hereby declared that the Parliament of Canada may from Time to Time make Laws in relation to Agriculture in all or any of the Provinces, and to Immigration into all or any of the Provinces; and any Law of the Legislature of a Province relative to Agriculture or to Immigration shall have effect in and for the Province as long and as far only as it is not repugnant to any Act of the Parliament of Canada."