My first pet was a rabbit and a few baby chicks for Easter.I was about 4-5 years old at the time. The baby chicks were so cute and cuddly.The rabbit was a different story. To me he was huge and frigidity and hard for me to hold, since he was so big.
Close up was too close for me at that age. I suppose he could feel my fear of him.
I still think about that rabbit to this day and I am a bit leary of them.I thInk you have to introduce a small child to these pets slowly and not as a gift in the sense that "okay here it is".