It is. Public inquiries are rare. The Canadian Judicial Council receives about 160 complaints against judges a year. Most of them are disgruntled litigants and are easily dealt with. Where there are rare cases where a complaint is sufficiently serious that a finding could result in the removal of a judge from the bench, it's open to the Canadian Judicial Council to require and call a public inquiry into the question. It's unprecedented right now, but there are three on the go, or there were three on the go.
On November 27th, 2014. See this statement in context.