I'm assuming you are looking for something cuddly
And I hope I am not being too forward here, but with her young age you will want to be certain that you are present whenever she holds and handles her new pet as children often don't understand that animals hurt too ;-)
Guinea pigs are WONDERFUL pets for children. They are very social (which is why I would recommend having 2 rather than just 1) and very gentle. They may experiment with their teeth, so be sure to teach her not to stick her fingers in or near their mouths. If held and loved regularly, guinea pigs will become very loved pets.
Another good choice are rabbits. Dwarf bunnies are small and make great house pets. Did you know that you can little box train a bunny? Then they can run about the house if you are comfy with that
I wouldn't go with a gerbil or a hamster at this young age. They often bite and are VERY fast if they get away. They also can get into small places and will be lost forever, much to the heartache of your little one.