My tiny pet / Jessie Hartland.

Enhanced descriptions from Syndetics:

A witty celebration of the tiny tardigrade, a microscopic creature that looks like a bear

Living in a tiny house has one huge drawback--no space for pets. So when a little girl's parents announce that it's time for the family to simplify, downsizing from a huge home in the city to a tiny house in the woods, it's quite a blow--after all, she's grown quite fond of her pet poodles, cats, tarantula, snake, hedgehogs, mice, birds, fish, octopus, rabbits, pony, pig, and turtles. Fortunately, she finds them all good homes, and she has to admit that she enjoys her new simpler life.
There's just one thing: She still really wants just one pet.
At first the answer is no. But using a little scientific savvy, she finds one that could be just the right fit--how could anyone turn down a pet smaller than an ant's eye that doesn't need special food or toys or walking, and will always be small enough to squeeze into their home, no matter how much they downsize?
Jessie Hartland creatively blends fantasy and science in a far-out story that bursts with exuberance. Her whimsical art celebrates one very thoughtful, persistent little girl and introduces readers to the tiny tardigrade, with its fascinating array of survival skills.