A rabbit is soft and fuzzy but they don't enjoy being cuddled. And one way they show their displeasure is to kick with the hind legs. That can cause some nasty scratches.
Chicks are cute but they grow into chubby chickens that poop a lot. Many folks get chicks or ducklings but then don't want them after they grow up.
She's pretty young still. If you want to show her how to care for a pet and enjoy their antics, a goldfish may be a good start. Not cuddly but she can help feed the fish, watch it swim in and out of its castle. Clean up would be done by the adults but that applies to a bunny too. When she gets a little older and understands how to handle a pet gently, then you can move on to a mammal. I think birds are great but not ideal for little children.
Your niece is way too young for a pet. My niece is three, and her parents owned a cat before she was born, so she's got one in the house, and she is not old enough to even understand how to treat animals properly.
I agree on the fish idea. She can feed the fish, it'll be fun to look at and watch, and it's not a huge commitment for her parents to have to look after it. In addition, fish are actually hypoallergenic pets! Birds and furry animals could all cause allergies.
Birds are a better pet for an older child, probably middle school age (so about nine at the earliest, depending on maturity of course). Even small mammals, like rabbits, hamsters, gerbils, and guinea pigs, should not be given to preschool aged children. They can be hurt very easily by little ones who don't understand how to be gentle, and they can and will bite when they are scared. They also have little nails that can scratch.
Have you talked to her parents about a pet? I would definitely do that first. Maybe they would like to have a rabbit as a family pet; maybe they would rather just have fish; maybe they don't want any animals in the house at all. If they rent, they may not be able to have animals in the house.
If the answer is no, why not get a stuffed toy instead? Children love such things. :)
Replying again - had a really interesting suggestion for a pet from my cousin! She has three kids, the youngest is about one now, I think. She suggested land snails. They can't get squished very easily at all, they won't hurt the child, and they are very cool to look at.
(I want some now, myself. But I am strange that way.)
thanks a lot for your advice!!! I think I´ll get her a goldfish then!! (something that if it dies it´ll be easy to replace-sorry if that sounded a little awful)...I will give her the responsability to feed it
I am now considering the land snails (I have seen a few terrariums online) , it seems like a pretty good idea...I really want one for myself now as well(reminds me of Spongebob squarepants pet - gary) so you are not that strange karalianne ...;)