Final answer:
The nurse should ask the pregnant client diagnosed with type 1 diabetes mellitus and experiencing nausea if she has been monitoring her blood sugar levels regularly.
Step-by-step explanation:
The most important question for the nurse to ask the pregnant client diagnosed with type 1 diabetes mellitus and experiencing nausea is, 'Have you been monitoring your blood sugar levels regularly?' This is because nausea can be a symptom of hyperglycemia, which occurs when blood sugar levels are too high. By asking this question, the nurse can determine if the client's nausea is related to her diabetes and if any intervention is necessary.