This is a stuffed animal I made for the birth of my boyfriends niece. It's made of baby-friendly material and has no dangerous pieces that could be swallowed or harm the baby in any way.
First, I made a cardboard template for the different pieces of the rabbit. Then I cut out the pieces of two types of fabric. For the belly and the inner ears I took a striped fabric with a strong contrast. I was told that babies like strong contrasts when they are very young, since their eyes are not yet capable of seeing tiny details. For the rest of the rabbit I chose toweling. The woman who sold me the toweling explained to me that this fabric is especially good for babies, because it shouldn't form lints, and you can wash it.
Now I made the ears. First, I sewed each of the inner ears onto one of the outer ears. I chose a zig-zag stitch which looks quite decorative I think. (First image in this step). Then i turned it around and sewed these ears to the other outer ears, so the seam would not be visible. I left one part of the ears open, so I would be able to reverse again. After that, I reversed the ears. For this step you might want to use a pencil or something, otherwise it's very hard to get the whole ears through that tiny opening at the bottom.
I first planned to fill the ears with pipe-cleaners, to be able to bend them in a funny way. But then i decided that it could be harmful for tha baby if its putting the ears in its mouth. If you like you can still do that.