The concept of a request body does not make sense with GET requests. A GET request is just that, a request to fetch a bit of information. You use the URL (combined with the query string a.k.a. GET parameters, if needed) to specify which piece of information you want.
HTTP specifies that the server should just pretend your body isn't there, which is exactly what you seem to be experiencing. To quote Roy Fielding:
Any HTTP request message is allowed to contain a message body, and
[the server] must thus parse messages with that in mind. Server semantics for GET,
however, are restricted such that a body, if any, has no semantic
meaning to the request. [...]
So, yes, you can send a body with GET, and no, it is never useful to
do so.
(via here)
For what it's worth, the RESTClient Firefox plugin seems to ignore what you put in the Body field if you're using GET. RESTClient uses Firefox's XMLHttpRequest, which apparently ignores body data if the method is GET. I can't say I disagree.