Laravel has a MVC design. If you can imagine to transform your code into MVC then the transformation should be easy.
My experience: transforming a project into a new framework/structure means a lot of redesign and rewriting.
If you have time and you want to learn a new, better way to program PHP then use Laravel ^^
If your site has the scalability to grow, then yes re-write everything in Laravel. You will find that Laravel 5 relies more on repositories, providers, etc more than Laravel 4. Like anything there is a small learning curve but it will be worth it. Hope all goes well in your project.
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