There are toy knitting patterns available for anything you can imagine from animals to vegetables. I feel much safer letting babies and young children play with knit toys than something manufactured that might be leaching lead or other toxic chemicals.
Most toy knitting patterns are likely to require double-sided knitting needles since you are working in small circles.
Remember that buttons and beads can become detached and are a choking hazard. It's best to use embroidery stitches for details, such as using French knots to make eyes and the satin stitch to make a nose.
The safest hypoallergenic toys are made with organic cotton yarn, but organic wool fiber that has not been exposed to harsh chemicals to remove the lanolin is also fine for most people, even some who think they have a wool allergy.
I have read that if you make a toy with wool yarn, stuff it with the typical polyester batting, and then throw it in the washing machine, the stuffing will help the figure keep its shape as it felts.
I have not tried this myself yet, and you'd want to be careful of any non-stuffed details like ears, but it sounds like a good technique.