No. 'Et dyr' has a neutral gender. That means it cannot end with anything other than 'et'.
For male words (en hest), they must all end with 'en'.
For female words (ei ku), you have a choice of using the female ending (kua) or the male one (kuen). This is ONLY the case for female words. You can also start it as a male word too, (en ku).
Some words, it's more natural to use the male or female version, but both are correct.