* A mother animal with her young: This is a general phrase that works for any animal.
* A parent animal with its offspring: This is similar to the first, but emphasizes that both parents could be present.
* A female animal with her litter: This is specifically used for mammals that give birth to multiple young at once.
* A bird with its nestlings: This refers to baby birds in their nest.
* A fish with its fry: This refers to baby fish.
You could also use the specific names for young animals, like a cow with her calf, a dog with its puppies, or a hen with her chicks.
The best way to describe an animal with babies depends on the specific situation and the type of animal you're talking about.