Can you have a vote of no confidence if you are not satisfied with the way the Public Trustee are handling / get settled your Father's deceased estate since he died?
A public trustee is supposed to be a neutral independent person/body given powers under state legislation to manage estates. Therefore, like Ivy asked, what is the act you are complaining of? If you have a complaint against the public trustee, you can direct your complaint to the Queensland Government and if you are not satisfied with their resolution/response, you can further complain to the Queensland Ombudsman.