It depends on the nature of the relationship with the person you are working for. If you are working as a consultant or independent contractor, the nature of the work that you are doing for them should be described rather specifically in the contract the two of you entered into. If you are an employee, however, your ability to negotiate the scope of the duties you perform should be somewhat flexible, depending on your relationship with your supervisor.
That being said, in the United States, most employee/employer contracts are "at will", which means that either party has the right to terminate the relationship without cause at any time. Using your example of a doctor doing nursing tasks, as an employee, you should factor in the associated costs of staffing a position created for the purpose of completing those tasks. Even if there isn't enough work to justify hiring another employee, the work still has to get done. However, you seem to imply a level of mismanagement on the part of the employer/client, rather than a lack of available resources to handle the smaller, lesser tasks. In either case, if you feel the work is truly "not part of your job description", then it would probably be in your best interest to engage your employer/client in discussion or to find work you deem more suitable.
As to the professionalism associated with making such a request, the act of asking doesn't necessarily challenge your professionalism, especially if you are an employee who is consistently being expected to perform these tasks at a lower rate of pay compared to the current market rate. At that point, a reassessment of your salary would not be out of the question. Without knowing the details of the working relationship, if you can't engage in a reasonable discussion with your employer/client, as previously mentioned, you may need to consider finding work with a firm which is more structured and aligned with the current job market regarding the assignment of duties and allocation of resources.