Great question! I believe the dropdown to select different content types to create is in qListView if you do not want to go that far from the OOTB list view. We do not have it in qListForm. If you have the qListView connect to the list that has several content types, this dropdown list under toolbar New gives you access to create new item based on different content types.
Now with qListForm, the content type is managed within the DisplayFields property where a dropdown list is available for content types with that list. Switch content types will reload the available fields to that content type which map the OOTB one.
Note that qListView toolbar New dropdown list when clicked, will by default opens up the form page NewForm.aspx and carry an extra query string named "ContentTypeId" with the proper content type associated with the selected content type from the dropdown. The qListForm is intelligent enough to check for this parameter. If this parameter is presented in URL, it will switch to use the display fields for that content type and you do not need to define and configure multiple qListForm for each content type.
In this case, you can simply configure a qListView to connect to the list having multiple content types. Configure another page or pages for NewForm, EditForm, and DispForm (or use existing ones by hiding OOTB web part). That is it and when you click New button from qListView for different content types, the form will render appropriate fields.