Hellobee Boards

I can only give you my sympathy. LO is almost 18 months and is terrified of dogs. She only likes them when they are FAAAR away. She used to be okay with them, but freaks out when they come close to her.

I'd actually rather have a toddler who was afraid of animals than one who wanted to walk up and hug strange animals all the time. Having owned a dog with aggression issues before who could get really unnerved by small children, I think there's really no reason a kid needs to much personal interaction with animals before the age of four or five, when they can understand and follow instructions.
If she's freaked out just by being around animals, I feel like at this point I'd probably work on making her feel secure around them, which will probably involve making her feel like she's in a safe spot where they can't reach her. I wouldn't force the issue, I'd work on teaching her that it's fun to watch animals from whatever distance she needs to be comfortable, and that there's no pressure to interact with them. Maybe do some zoo or petting zoo visits where you reassure her that you're only there to look at the animals and that they won't get near her or touch her if she doesn't want, and work on getting her to enjoy watching animals before you try interaction? That way, she can feel like she's the one in control of the interaction, whereas if an animal actually comes up to her in person, at this age she's not at all in control of what the animal does or does to her (even if it's just sniffing or being totally friendly). I would imagine that once she's older (and has more of a size differential with animals, and can move more quickly, etc.) she would feel more confident in her ability to control the interaction and direct it into a comfortable experience for her, which she can't do at this point.

DD is two and loves animals in the form of pictures and toys but in real life, she is TERRIFIED! Even at the zoo - she doesn't understand the concept of cages and windows - real life animals freak her out. I am very sensitive to protecting this fear from a childhood experience that I had (long story short: I was three and we were hiking and the trail was littered with slugs and worms and I freaked out but my father made me walk through them thinking I'd overcome my fear. Instead, I had nightmares on and off for years and I STILL have panic attacks when it rains and the worms come out).

So anyway, I would still introduce your bunny and the neighbour's cat to your toddler but still be wary that her fear is real. Poor thing!