CERT training can't prepare you completely for a disaster. Nothing can really do that. But CERT training does teach you five basic skills to help you survive and enable you to help your neighbors to survive. What it doesn't address, but something you need to address, is what to do with your pets in the event of a disaster. Be forewarned, at this point in time, there is no good answer.
 
Fido might be okay if you don't have to evacuate your residence. A dog, or cat for that matter, can adapt to  a disheveled house or changes in the backyard caused by downed trees as long as the family pack is intact. But if evacuation is required, understand that no pets are allowed in emergency shelters. And that's a problem. Your pet will be on its own for an unknown period of time. There is no good way to ensure it gets daily food, water, and shelter. Many cats and dogs do just fine living off the land for a few days, but young pets, old pets, or pets that require medication may have problems.
 
The more difficult problem is with exotic pets like snakes, spiders, lizards, ferrets, exotic birds, and fish. The fish could be in an aquarium, a bowl, or a waterscape.
 
Certainly any exotic fish, freshwater or saltwater, will not survive for long if the power goes out and the aquarium aerator shuts down. Goldfish and coy in waterscapes will probably fare a little better as long as the waterscape structure isn't compromised and the water leaking out.
 
It is possible that pets like snakes, spiders, lizards, ferrets, and birds may survive the initial disaster. But they would probably do so by escaping into the "wild." Obviously, this has its own set of problems. Some non-native species are simply unprepared for the native climate and available food supply and will eventually die off. This is a sad way to lose a pet, but it avoids introducing non-native species into the native habitat. Those exotic pets that don't fall into this category, could survive and prosper, meaning they could proliferate in the native habitat, out-compete native species for available food supply, and ultimately drive them into extinction. Think of how nutria have taken over the waterways.
 
If anything, wondering about what to do with your pet in the event of a disaster, and knowing you won't be able to take it with you, may influence your choice of a new pet as well as help you develop a plan for how to deal with it should a disaster strike.