Animals
Animals have gone into space like Laika the Dog first living animal to go into orbit aboard Sputnik 2 on the 3rd of November 1957
The old USSR flew dogs into space 57 times during the 1950s and 1960s the USSR used dogs for sub-orbital and orbital space flights to determine whether human spaceflight was feasible.
Also a number of Monkeys and apes have been used for test flights.
To date, seven national space programs have flown animals into space: the Soviet Union, the United States, France, Argentina, China, Japan and Iran.
The first animals sent into space were fruit flies in 1947.
Testing of mice and other rodents have been used for experiments aboard the ISS along with Fruit flies, mice, monkeys, chimpanzees, guinea pigs, rabbits, frogs, reptiles and a variety of insects.
Other animals in space include a cat and tortoises, wasps, flour beetles, wine flies, spiders, snails and meal worms.
Fish include carp, medaka, oyster toadfish, sea urchins, swordtail fish and brine shrimp.
But the main reason now is the use of animals for food. Priority will be plants due to the per square meter required, food requirements for the calories per gram produced, so the first colonies will be vegetarian.
Animals on Mars unlike some Fish require large amounts of food production
Animals for Meat
Animals will not go to Mars until a fully developed agriculture is plentiful enough to support the feeding of them.
I suspect one of the first animals on Mars will be chickens. Chickens are very efficient at turning what they eat into protein and chicken manure can be converted into biochar (which is a charcoal like product) useful for growing crops, Also the benefit of possibly transporting eggs to Mars, a lot of research will be required.
An interesting experiment was carried out in 1989 called “Chix in Space” after a second mission on STS 47 in 1992 led to the “Avian Development Facility” has been taken to the ISS in 2001 for ongoing study.
Artificial meat
One possibility maybe the production of artificial meat but current research is very power demanding.
An interesting article 'The Race to Make a Great Fake Steak'
Chickens
I have been trying to look into the possibility of keeping chicken eggs alive to transport to Mars but that is not looking good so far,
To the Moon is fine just keeping them chilled should work.
Another possibility could maybe to keep chickens in an artificial gravity system so they can drink properly.