Most toy stores and toy manufacturers don't have much of a markup on their products. Expect after all expenses are in to make no more than a dollar or two on each stuffed animal that you sell if you are selling new, non exclusive merchandise. This means that you need to deal in volume in order to make this a viable business. If you want to sell stuffed animals that you make yourself, you can typically make significantly more money on a per item basis, but remember that you are then limited in the numbers you will sell, both because you simply cannot make that many stuffed animals in any given day and because you are now dealing in a boutique market where you are selling a certain mystique about the hand crafted "one of a kind" toys that you have to offer rather than in the general retail market where parents buy their kids a stuffed animal.
If you like the idea of trying to sell stuffed animals but are not sure about the pre-made market and the antique market doesn't really do much for you either, consider instead opening a franchise of build a bear. These places allow kids to custom design a stuffed animal of their own and then fill it with foam filling on the spot.
You may also want to look into working with taxidermy. While not nearly the same thing as selling stuffed animals, it is a related field where people collect the items, though in this case you are working with animals that were once live.
While the picture is positively creepy looking on this article, it does have some great advice on getting into the business of selling stuffed animals.