I've been playing a guitar for about seven months, and I've reached the point where I can play Brown Eyed Girl (G, C, D, and e minor chords) and House of the Rising Sun (am, C, D, small F, and E chords) competently. So what other song should I learn to play? At this point, I feel a lot of new songs that I want to learn how to play are either too difficult or too easy.
This doesn't answer your question, but it's worth considering. Don't learn something with the chords you know in mind. If you do that you have no reason to learn more.

Try learning something with a new chord in it to help you practice transitioning through the new chord shape as well as lock it into your memory.
i agree with shiggityswah. learn new chords and keep on playing the same stuff you already know., maybe its time for you to learn B7, F7, and G7. before you try Barre chords.
Try some of Zeppelin's acoustic stuff or get into some guitar picking songs. Learn the Travis picking method. A good one to use it for is Little Black Submarines by the Black Keys or Just Breathe by Pearl Jam.