Origin of "tootsie" or "tootsy" (foot)

Etymonline:

tootsy
also tootsie, 1854, baby-talk substitution for foot. Candy bar Tootsie Roll patent claims use from 1908.

And it sounds like a combination of toe and foot.

The early instance of tootsy-pootsies that Callithumpian notes in a comment beneath the posted question is evidently from "The Physiology of London Evening Parties," part IV, in Punch, or the London Charivari (January [?] 1842), subsequently included (with minor revisions) in volume 2 of Albert Smith, The Wassail-bowl: A Comic Christmas Sketch-book (1844):

At length all the preparations are completed, and a temporary quiet reigns through the house; but it is like the lull of the elements after a boisterous day in March, before it begins to rain. The last ring has brought the last parcel to the door, which of course ought to have arrived first in the morning; the small children have been rapidly undressed and put to bed with the wild notion that they will stay there, and not walk calmly down stairs some three or four hours afterwards in their night-gowns, with their little naked white tootsy-pootsies (the nursery patois for tiny feet) pattering on the cold floor-cloth: the governesses in families where they are not going to give a party have marched all their young ladies, hoops, and la grace sticks, out of the square, and are thinking about changing their collars for dinner; the last views have dissolved, the diving bell of the Polytechnic Institution has gone down, and the Royal George has been blown up for the last time; the Westminster idlers have disappeared, no one knows where, nor ever will; and the last clang of the milk pails has echoed down the areas; in fact to the majority of the world the labours of the day have concluded, excepting policemen, actors, medical men, waiters, people who give parties, and hair-dressers, who attend by appointment an hour before the time of receiving company, pour coiffer les dames.

The use of tootsy as a familiar word affection seems to have occurred at about the same time. From "Matrimonial Dictionary," in Punch (September 26, 1846):

TOOTSY, MOOTSY, and all words ending in tsy, are terms of great endearment. The exact meaning of them has never been ascertained. They are never heard after thirty.

Indeed Albert Smith, The Struggles and Adventures of Christopher Tadpole at Home and Abroad (1847) has a character call his wife "Tootsy," with this brief explanation:

"Well, I don't quite know, Tootsy,"—it was a relic of their honeymoon, that "Tootsy," which Mrs. Gudge still liked to be called. "I've met 'em before though, I think at Sir F's."

I would be remiss not to cite the entry for tootsies in John Hotten, The Slang Dictionary (1864):

TOOTSIES, feet, those of ladies and children in particular. In married life it is said the husband uses this expression for the first six months, after that he terms them HOOFS.