I am an animal person, as many people are. There are so many people who adore cats, dogs, birds, and everything in between. But please remember - getting an animal is a lifelong commitment as long as they live. This includes animals bought as gifts for Christmas.
I'm of the opinion that if someone adopts a pet, they are responsible for that animal no matter what, barring things such as homelessness and death. I have gotten pets and I have thought long and hard about how to take care of them, what potential health issues they may eventually have, and how their personalities will mesh with my lifestyle. Getting a pet is more complicated then picking the cute Siberian Husky because it looks like a wolf and has fuzzy ears. Getting a pet is more complicated than "it seemed right!". Getting a pet is more than getting one to shut up Jimmy because he does this every year.
Please don't give your child a pet for Christmas. This includes everything from fish, bunnies, cats, dogs, birds. Let them visit a relative who has toddler or child tolerant pets. Maybe let them volunteer to help animals or raise money for animals. Unless you, as a parent, fully intend on taking care of this animal, and socializing this animal, and training this animal, and feeding this animal decent food, and take care of the vet bills for this animal, then by all means - get an animal. However I'd advise you to wait until after Christmas, because most animals that are bought for Christmas eventually end up on Petfinder shortly thereafter.
Christmas is only a few weeks away, and every year, thousands of animals are returned or sent to shelters. A dog is not a gift, a dog is a responsibility akin to having a child. A cat is not a gift, and kittens are little ninjas that will destroy your furniture underneath all of that adorable fuzz. Birds can be as smart as toddlers and bunnies have their own set of rules, including that other animals might view them as prey (in particular, dogs or cats you already have might want to eat him). Fish cannot be kept in a bowl, including bettas and goldfish, and some need special care or big tanks.
Please, as a person who has rescued animals from all different types of situations, don't adopt for the holidays. Stick to Toys R Us instead.
You surely know what it's like to be responsible for a child or a marriage or a relationship. That same maturity needs to apply to all life. There are so many things a potential pet owner needs to think about, and Christmas is definitely too busy of a time to start.
Pets are responsibilities. They are not gifts.