Is it possible to transfer my local installation entirely to the server?

There are a couple of methods you can try. Depending on whether you want to keep your online data or not.

Export Tool

There is a tool for exporting data from one installation to another, under the Tools menu. Head over to Tools > Export and select All content from the options. Click the Download Export File and save it.

Now, head over to Tools > Import in your published blog. Choose the file you saved from the last step, and import your content into the online blog.

Manual Transfer

You can also copy your entire WordPress directory via FTP, and then change the WordPress Address (URL) & Site Address (URL) in the settings from localhost to http://example.com. This however will override your existing content, but your plugins and themes will be uploaded too.

Plugins

To transfer the plugins, simply copy them to your online server via FTP, and activate them from the plugins menu. Their settings will not be preserved, but some plugins themselves offer exporting their data. You may however be able to copy their data from your local database to your online database.