Yes! Lots of people do that for various reasons. Some because they want to bury their pet in their backyard but the animal dies during winter / when the ground is frozen so they have to wait a few months. Others do it while preparing to send their pets to a taxidermist or cloning company. And others do it just because they need a little longer to say goodbye and sit with their pet's body as they process their death -- very natural and normal, like how a lot of cultures have wakes/viewings for human bodies after someone dies.