How do I add a vertical line separating the Don't know response from the other responses to my Likert-style question in my Qualtrics online survey?

You can use html like

<div class="QuestionBody">
    <div class="ChoiceStructure dontknow">
        <input type="radio" name="QID1" value="1">
        <span>Strongly Disagree</span>
    </div>
    <div class="ChoiceStructure">
        <input type="radio" name="QID1" value="2">
        <span>Disagree</span>
    </div>
    <div class="ChoiceStructure">
        <input type="radio" name="QID1" value="3">
        <span>Neutral</span>
    </div>
    <div class="ChoiceStructure">
        <input type="radio" name="QID1" value="4">
        <span>Agree</span>
    </div>
    <div class="ChoiceStructure dontknow">
        <input type="radio" name="QID1" value="5">
        <span>Don't know</span>
    </div>
</div>
 

@politicalcyclist Probably the codes are not working because you are using a different theme/layout. It would help if you could share the preview link of your survey.