[Vuejs]-Laravel and vue not submitting data not querying data from database

You need to respond with Access-Control-Allow-Origin header when accessing backend from differend domain. In this example the value of Access-Control-Allow-Origin must be http://localhost:8000.

Adding header to your response is quite easy in laravel: https://laravel.com/docs/5.7/responses#attaching-headers-to-responses

You can also use this library: https://github.com/barryvdh/laravel-cors