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There was a reason the nursery rhyme didn’t mention an egg. According to Wiki, the earliest known publication was in 1803:
According to the Oxford English Dictionary the term “humpty dumpty” referred to a drink of brandy boiled with ale in the seventeenth century. The riddle probably exploited, for misdirection, the fact that “humpty dumpty” was also eighteenth-century reduplicative slang for a short and clumsy person.
Although there are other unproven theories that the rhyme references an historical figure or event, Humpty Dumpty was merely a riddle of the “What Am I” sort, and the answer was “an egg.” (And ten dozen guys couldn’t figure out how to make an omelette?) Try this one:
I am white
And wet to touch;
I can blind
If you stare too much.
Tacky Raccoons 