How to simulate selecting from dropdown in Jest / enzyme testing?

Try this approach:

      wrapper.find('option').at(0).instance().selected = false;
      wrapper.find('option').at(1).instance().selected = true;

You can trigger a change event since you have your this.handlechange trigger onChange:

const component = mount(<MyComponent/>);
component.find('#dropdown').at(0).simulate('change', {
    target: { value: 'item1', name: 'item1' }
});

I would say you have to add .at(0) because Enzyme will find a list of values even if you only have one element with that ID.