You'll need [QSA,L] to append the original query string back on.
By the way, be clear what a rewrite does. It takes a URL request and translates that into an internal filepath. So, it is right to show a domain name in the example requested URL, but for the filepath example don't specify a domain name - there isn't one, it is just a filepath inside the server. That is, the target of the rewrite is NOT another URL. URLs only exist outside of the server; out on the web. Inside the server there are only filepaths.