The phrase “easy as rolling off a log” means: Nothing could be easier; the simplest action possible.
Early American colonists, probably, moving into a wilderness with a hundred things to be done at once by both husband and wife, sought desperately for a safe and dry place to “park” the baby temporarily.
Just as a modern couple would do on a camping expedition, undoubtedly they would place the infant on a log, “just for a minute.”
The little round bottom of the baby, however, was no more stable on the big round log than a marble would be on a child’s balloon.
At least, this could have been the way the goes back into colonial days.