Could this be the novel Space Prison/The Survivors (available at Project Gutenberg) by Tom Godwin. Published in 1958, it is based on an approx 30 page short story called "Too Soon to Die", published in Venture magazine, but lacks several of the features of the novel.
The general plot of the novel is below, the short story follows that plot, but without the help of the animals, so differs from your question.
In this story Earth is under attack from an alien race called the Gerns. The Gerns capture an Earth spaceship taking colonists to another planet and maroon the colonists on a planet called Ragnarok.
Ragnarok is a hell-hole; high-gravity; burning hot in summer (lasts the equivalent of 2 Earth years I think), totally frozen in winter, has a ravaging disease, incredibly ferocious animals (prowlers - half-wolf/half tiger intelligent; unicorns - herd animals that trample anything that attacks them, both species are telepathic). There is also no metal on the planet and little edible food.
The survivors of the initial stranding find ways to adapt to the environment and travel around parts of the planet looking for food and resources - both distinctly lacking where they are. Eventually, on one of these expeditions, they find some telepathic animals called Mockers. Mockers are capable of picking up something that someone has said and transmitting it to another mocker, who then repeats it out-loud. They are described (bolding mine):
They emerged into full view; six little animals the size of squirrels, each of them a different color. They walked on short hind legs like miniature bears and the dark eyes in the bear-chipmunk faces were fixed on him with intense interest.
The survivors manage to domesticate the mockers and also manage to help rescue some prowlers from unicorns and domesticate them as the prowlers start to trust the humans. They communicate with the prowlers telepathically. They also manage to capture some Unicorns, and semi-domesticate them, but they still remain aggressive and uncontrollable without the use of force.
Eventually, some generations after the initial marooning, the descendents find a source of metal and make a transmitter, which works by radio and will take ~30 years to get it's signal to another world. They push the button and send the signal "Ragnarok Calling", which eventually attracts a Gern spaceship. The spaceship is then captured by driving the unicorns at the invading Gerns and using the prowlers to hunt down survivors and get on-board the ship, which they capture using their high-gravity reflexes and strength.