It is possible. Laravel is just a PHP framework, and it is easy to learn and make it do whatever you want to do.
There are many ways you can approach this:
You would need payment processing system (or use sprite for this), but you would definitely need to track sales and revenues, etc, and this can easily be done in Laravel.
You would need phone app (like Uber or Lyft does), where clients can track the taxi, and the best way I would approach this is using google maps API (This is not Laravel)
Another nice to have system (in Laravel), a reporting system, to see how many people booked, how many canceled, and how many trips got fulfilled.