If they don’t, I guess that there are no animals in heaven.
All living things have souls, but only angels and humans have spiritual souls. Animal and plant souls are material principles that cease to exist at death. Angels do not die, and human souls survive the death of the body.
We do not know God’s plans for creation, including animals and plants. A hint that creation may be glorified at the end of time can be found in the Catechism of the Catholic Church:
For the cosmos, revelation affirms the profound common destiny of the material world and man:
For the creation waits with eager longing for the revealing of the sons of God … in hope because the creation itself will be set free from its bondage to decay. … We know that the whole creation has been groaning in travail together until now; and not only the creation, but we ourselves, who have the first fruits of the Spirit, groan inwardly as we wait for adoption as sons, the redemption of our bodies (CCC 1046).
The visible universe, then, is itself destined to be transformed, “so that the world itself, restored to its original state, facing no further obstacles, should be at the service of the just,” sharing their glorification in the risen Jesus Christ (CCC 1047).
In short, it is possible that God may re-create and glorify creation, including animals and plants. We may hope then that it may be possible to meet deceased animal friends in the next life.