Mkay, in 15 minutes, this is what I got:
Melodyandotherstuff.org
First, I doubled the length of the melody for which the song is named, and doubled the tempo accordingly. I tend to stay away from one-click note length unless the song is faster, because it always results in a cut off sound that is not becoming to your pretty scales.
Afterwards, I added the chords. With your melody playing out at middle C, I thought the chords would sound like a bassline, so I put them an octave above.
Basic music theory lesson: If you have some chords, and the higher note holds while the lower not descends, it sounds pretty and stuff. High chords at the end of a phrase sound triumphant and painful (in a good way), do them in your song.
You're in a major chord, C major to be exact. It's what you get if you play a melody on just the white notes of a keyboard (which in fact you may have done). Stay with them always and forever until the song is done, unless you plan for a chord change.
You could add a third note to the chord, that would sound nice. Just change the note until it sounds nice (the best way to make chords :3).
I spent 5 minutes making a bassline, but I didn't like it so It's gone now.
Just stick with longer notes than the melody and some gaps in between, I'm sure you'll do fine there. A mix of double and quadruple the melody's note length should sound good.
Anything else you'd like advice on?