I am going to contradict the other answer. Humpty Dumpty may not have been an egg at conception, but he was certainly one by 1835, thirty years before Lewis Carroll wrote Alice in Wonderland.
There was a long satirical poem published in 1835, Child Capone's Nonage, by A Monk, which you can find on Google books, which has a footnote which starts:
“Humpty-dumpty sat on a wall,
Humpty-dumpty had a great fall:
Not all the King's horses and all the King's men
Could set Humpty-dumpty right agen.”This nursery rhyme upon an egg, which every body remembers, represents, under a beautiful allegory, the easy lapse of a child from his early position of virtue, and the vast difficulty of reclaiming him at school and college, even though these may have been founded and endowed by kings.
It's not clear to me whether the footnote is serious or not — I expect not.
Let me remark that the riddle is not quite as hard to guess as it might seem to modern readers. Before the riddle branded Humpty Dumpty as an egg forever, Humpty Dumpty meant a short, fat person. For example, Google books finds the 1828 book The Dialect of Craven, in the West-Riding of the County of York by Mark-William Carr, with the definition:
HUMPTY-DUMPTY , Short and broad. "He's a lile humpty-dumpty fellow"
and an egg is indeed short and broad. So, even though the word "humpty-dumpty" originally meant a short, plump person rather than an egg, it may be that the poem originated as a riddle whose answer was an egg.