What is the animal Alice is riding in Alice in Wonderland?

In the book, the White Rabbit is the first Wonderland animal that Alice sees, however she doesn't see him in Wonderland, but in the real world. She follows him into Wonderland, and just catches a glimpse of him as he hurries down a corridor, so he is also the first animal she sees in Wonderland.

The first animal she actually meets is the Mouse, who has fallen into the pool of tears along with Alice.

As to whether the animals are particularly strange is perhaps a matter of opinion. It is certainly strange for animals to have human characteristics, such as speech and clothing (and pocket watches), but the majority of animals Alice encounters are relatively normal - cats, dogs, birds etc.

After meeting the mouse, she meets a dodo, which could be described as strange as dodos are extinct. Towards the end of the book she meets a mythical animal, in the form of the Gryphon, and a fictional animal, created by Lewis Carroll, the Mock Turtle. They are definitely strange.