The earliest match for duck's egg in the sense of a mark of zero that I've been able to find is from a letter to the editor of the [London] Morning Advertiser (August 28, 1848) [combined snippets, paywall blocked]:
...to be the Miss Lydia filly by Don John, who was backed for a fortune to win the Oaks, and again by a few, rather heavily, for the Goodwood Cup, but here she was absolutely friendless. Mr. YVrather [?], her proprietor, was fined for the nondeclaration of colour, which, however, was no apology for the omission of the name on the card, as there had been no declaration of forfeit, and I must again anathematize the return lists, which get worse and worse each day, winding up with a start of twenty for the race, in lieu of ten, and put a duck's egg, alias 0, to Canezou amongst others, who were quietly reposing in their stables. Such awful blundering is mischievous, disgraceful, and perfectly unpardonable; and if they cannot find a printer in the North who knows his business, let them send to the South, they do for their judge and starter.
This instance, besides being eleven years earlier than the one cited by the OP from the New York Times on September 28, 1859, is also of interest because it involves horse racing rather than cricket. This suggests either that the letter writer was applying an expression from cricket to the track or that the usage originated outside cricket and migrated there subsequently.
The Wikipedia entry for cricket indicates that it dates to the sixteenth century, meaning that the sport emerged in England hundreds of years before the earliest instance (so far) of the slang term "duck's egg" appeared.