Every single noun in Danish has a grammatical gender. There are two grammatical genders in Danish: common gender (-n words) and neuter gender (-t words).
For example, katten (the cat) is a common gender noun because its definite form ends in -en. You would also say en kat (a cat).
Dyret (the animal) is a neuter gender noun because its definite form ends in -et. Et dyr (an animal), dyret (the animal).
In general, animals/living things will be common gender nouns (nouns which definite forms take an -en at the end, e.g. hesten, katten, fuglen), but sometimes they will be neuter gender (hamsteret, dyret). So it depends on whether or not the word is common gender, neuter gender, or even plural, not how they can be grouped together.