How to test an unmounted React component's method that relies on setState?

I have implemented a component (for a typing training app) which tracks key presses on global scope like this:

class TrainerApp extends React.Component {
    constructor() {
        // ...
        this.handlePress = this.handlePress.bind(this);
    }
    handlePress(event) {
        const pressedKey = event.key;
        const task = this.state.task;
        const expectedKey = task.line[task.position];

        const pressedCorrectly = pressedKey == expectedKey;
        this.setState(prevState => {
            const newPosition = prevState.task.position +
                (pressedCorrectly ? 1 : 0);
            return {
                // ...prevState, not needed: https://reactjs.org/docs/state-and-lifecycle.html#state-updates-are-merged
                task: {
                    ...prevState.task,
                    position: newPosition,
                    mistakeAtCurrentPosition: !pressedCorrectly
                }
            }
        })
    }
    componentDidMount() {
        document.addEventListener(this.keyEventTypeToHandle,this.handlePress);
    }
    componentWillUnmount () {
        document.removeEventListener(this.keyEventTypeToHandle,this.handlePress);
    }
    ...
}

and I'd like to write some unit-tests using Jest. My initial idea was:

describe('TrainerApp.keyHander should',() => {
    test('move to the next char on correct press',() => {

        const app = new TrainerApp();
        app.state.task.line = 'abc';
        app.state.task.position = 0;
        const fakeEvent = { key: 'a' };

        app.handlePress(fakeEvent);

        expect(app.state.task.position).toBe(1);
    });
    ...
});

but the problem is app.handlePress relies on usage of this.setState which is not defined when the component is not mounted yet. Of'course I can modify the app like this:

test('move to the next char on correct press',() => {

    const app = new TrainerApp();
    app.setState = jest.fn(function(handler) {
        this.state = handler(this.state);
    });
    app.state.task.line = 'abc';
    app.state.task.position = 0;
    const fakeEvent = { key: 'a' };

    app.handlePress(fakeEvent);

    expect(app.state.task.position).toBe(1);
});

but this seems a very fragile approach (here I rely on the fact that .setState is called with the function argument while it can be called with just newState argument and hence I'm testing implementation details, instead of just the behaviour. Is there a more robust way to test this?