Yes. All officers of Parliament should have those powers, but she needs not only to have the power but also to actually be mandated to impose a penalty for every violation.
She could have found those almost 20,000 lobbyists guilty of violating the Lobbyists' Code of Conduct and issued a public ruling that would have identified them and named and shamed them, and she didn't in any of those almost 20,000 cases of violations. If you give her the power to levy administrative monetary penalties, from her record she won't use it 99.9% of the time, so she should be required to issue a penalty in every single case of a violation.