You can send your idea to more than one editor at once. But be sure to tailor each letter so that it fits the publication. Otherwise it might read like a form letter.
You may or may not hear back from the publication. If you’ve included your SASE, you might get a rejection letter if your idea is not accepted. You’ve just got to keep trying until you get the one editor that needs your writing.
If you get a rejection letter, it’s unlikely that it will explain why your idea was not accepted.
If you get the go-ahead from the editor, you should be prepared to get your piece written immediately. There may be a deadline.
So you see, a query letter is more than just a great idea, although that is where it starts. Make it professional, polish it until it shines, and you will be on your way to getting published.