Moving Laravel 5.4 site from localhost to online shared server (with Laravel already installed and working)

I've got Laravel 5.4.15 on localhost with my site working fine, and Laravel 5.4.9 on my hosting account (I have FTP and SSH access and Laravel test page up and running). Just wondering how to move my site onto the online host.

I don't want/need to replace the entire Laravel structure on the online host given it's already installed by the host co and working (if it ain't broke don't fix it). Just wondering what needs FTP'ing up to the site.

It's a pretty simple app. so I'm just using some Models (app/), controllers (app/http/controllers), various css/js/fonts/images (public/), some blade templates (resources/views/) and some routes (routes/).

On the database front, I'm using Eloquent and have various migrations in the database folder which have created then made various changes to the db but can't I just export the whole Laravel DB from mysql on my localhost and import into the one online without having to run all the migrations (could get messy). Presume I need to change some config files too? Within the Laravel folders, structure seems exactly the same on localhost and online.

Thanks for any tips.