Pretty much every character in this movie is an "animal," and one of the major plot points is that the leader of the migrating herd (Kron) has a tendency to abandon the "weaker" members of the herd.
The only character who counts as a "pet" is Url, the dog-like Ankylosaurus. Thankfully, he never gets abandoned by his owners Baylene and Eema (if you can even call them "owners." The Goofy and Pluto logic in this movie gets weeeiiird.)
At the beginning of the movie, a massive, predatory dinosaur (Carnotaur) launches an ambush on an unsuspecting community of herbivores.
When Aladar and the lemurs encounter velociraptors in the desert, one of the raptors intimidatingly lunges at Aladar's face and roars. We see this from the perspective of Aladar.
Although there are no suicide attempts in this movie, at one point the main character (Aladar) does enter a state of mind that some might interpret as suicidal.
Towards the end of the movie, Aladar and his allies get trapped in a cave. The usually optimistic Aladar grows hopeless and claims that he's "not meant to survive." Thankfully, Aladar is talked out of this mindset by Baylene, who motivates him to keep going. It's a very touching scene.
This is the basis of the main conflict. Kron's leadership is based on the philosophy that any dinosaur that cannot keep up with the herd has to die to ensure the survival of those who can, while Aladar argues that the herd would do better to stand together and protect everyone. The outcome ultimately favours Aladar.
At the end of the movie, the protagonists (and the rest of the herd) find the oasis that they've been desperately looking for, with the lemurs finding more of their kind and the dinosaurs watching their long-awaited eggs hatch.
The movie ends with the animals letting out a triumphant chorus of roars and howls.