Neither Quebec nor any other province requires any permission of any sort from the federal government to regulate any lending industry in its province within the 60% limit set by the Criminal Code. The Criminal Code otherwise applies to all lending transactions in Canada, so if a province wishes to allow lending transactions in excess of 60%--and that's what we're talking about with payday lending--then the Criminal Code otherwise simply prohibits that and makes it a criminal offence.
Unless there's an exemption in place, the provinces simply are not in a position to do that.