In the Annotated Mother Goose, Martin Gardner claims that the poem, which first appeared in 1810 but was much older, had always been intended as a riddle to which the answer is: an egg. The OED gives two definitions of the term, though doubts that the two are related. The first, dating to 1698, is "a drink made with 'ale boiled with brandy.'" The second is the Humpty we're more familiar with now:

A short, dumpy, hump-shouldered person. In the well-known nursery rhyme or riddle (quoted below) commonly explained as signifying an egg (in reference to its shape); thence allusively used of persons or things which when once overthrown or shattered cannot be restored.

So it hedges on the whole matter of the egg a little. The first citation that explicitly states HD was an egg is indeed from Through the Looking-glass.

A few other theories have been advanced about the possible origins of the rhyme. Two are from the English Civil War: in one Humpty Dumpty was the name of a "tortoise" war machine used at the Siege of Gloucester, and in the other HD was the name of a particularly large cannon employed at the siege of Colchester. Finally, there is the theory that HD is meant to be Richard III (of "my kingdom for a horse!" fame), who was slandered by the Tudors and later Shakespeare as a humpback.

Of course, it's not difficult to imagine that the rhyme worked both as historical doggerel and a riddle all at once.

Sorry I can't give you a more definitive answer. When it comes to nursery rhymes, origins get pretty nebulous (see "Mary, Mary, Quite Contrary" or "Jack and Jill" or really most of them).