A ballad, simply put, is a song (or a poem) that tells a story. "She's Leaving Home" certainly fits this requirement. In modern parlance, "ballad" usually means a slow, romantic song; if you're comparing a traditional ballad to this sort, you'll have an easy time of it, since this song is rather anti-romantic. (It's slow, yes, but isn't designed to melt a lover's heart.)
A traditional ballad, however, has far more requirements. The subject of a ballad itself is fairly unlimited, but a traditional ballad normally focuses on histories, legends, fairy tales, animal fables, and tales of outlaws, star-crossed lovers, or even jokes; in the case of all but the last, the themes are usually tragic--someone's death or downfall (like "John Henry"). The histories were usually about famous, important people (aristocracy), but not necessarily.
The writer of a traditional ballad was almost always lost to history; the ballad comes to us anonymously. "She's Leaving Home" does not fit this requirement, either.
"She's Leaving Home" is not so much about a person as it is about the freedom she gains by leaving behind all that she knows and loves. It could be about anyone. It recounts an experience (with an implied happy ending, as opposed to tragic) more than a simple tale of a specific person; were it about a specific person, we'd be given a name.
The structure of a traditional ballad quatrain stanzas (that is, with four lines each). "She's Leaving Home" has six. The rhyming structure of traditional ballads is ABXB (where X is any word which may or may not rhyme with A); compare this to the rhyming structure of your song. Also, the lines of traditional ballads are usually three to four metrical feet long; again, "She's Leaving Home" has much longer lines.