Meet the rabbit
Pick this rabbit up and the first thing you notice is the fur. It's soft and brown, with floppy ears and a fluffy tail that children tend to stroke before they've even put a hand inside. Slip a hand in and the mouth opens and closes with the movement of the fingers and thumb.
That movement is what makes it a real puppet rather than a soft toy with a hand-hole. Your child controls the mouth, and the voice and personality are all theirs.
What the puppet builds
Operating the mouth is a repeated open-and-close of the thumb against the fingers. That is the same pinch-and-release pattern that builds the hand strength and finger control needed for holding a pencil in prep. Most children don't notice they're practising, because they're busy making the rabbit talk.
There's a language benefit too. Around 3 years, children begin to narrate, ask questions and act out conversations. A puppet gives them a character to speak through, which helps hesitant talkers try out new words and longer sentences without feeling put on the spot.
How it gets played with
One afternoon the rabbit is a shy visitor at a tea party. The next day it's the patient in a vet clinic, or a character in a bedtime story your child tells you. It's a gentle character, so it suits calm, nurturing play as well as performing.
It makes no sound of its own, so the voice is always your child's. It works well alone in a bedroom or playroom, and it's even better as a two-person game, with a parent or sibling holding a second puppet for a back-and-forth conversation. Play grows with your child: at 3 it's greetings, animal noises and simple pretend scenes, by 4 or 5 it's short stories with a beginning and an end, and by 6 it's scripted puppet shows for an audience.
Safety note: not suitable for children under 3 years due to small parts.