If your code isn't (yet!) very complicated then you're probably best doing 'acceptance' style tests - ie, replicating browser-like actions that you'd do yourself to check the code was working. So in your test you might have something along the lines of :
// test login
// create a user 'tester'
$this->visit('/login')
->type('tester', 'username')
->type('thepassword', 'password')
->press('login')
->see('Welcome tester');
// test quiz
// create a quiz question record
// create a test user
$this->actingAs($user)
->visit('/quiz')
->see($question1->title)
->select($question1->correct_answer_id)
->press('Answer')
->see('Correct!');
// and the equivalent for picking the wrong answer
And you write those tests before the code for your app in TDD. Once the code gets a bit bigger and you've maybe looking to extract/refactor things then you can look at writing 'unit' tests for the way you expect that code to run - then write the code. Then you can still run your original acceptance tests and see they pass along with the new ones for your new code.
Generally you wouldn't test the basic functions of eloquent (or other aspects of the framework). But, for a contrived example, maybe your app creates a DB record in a mailing list table when a user registers so you might want to do a test of :
$this->seeInDatabase('mailinglist', ['email' => $testuser->email]);