An egg, a little deformed dwarf. Dumpty is a corruption of dumpy (short and thick). A dump is a piece of lead used in chuck-farthing. Humpty is having a hump or hunch. The two mean short, thick, and round-shouldered.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Humpty Dumpty from Fact Monster: