You answered your own question when you asked "God wouldn't give us these precious little animals in this life and not make some kind of accommodation for them in the next life, would he?" He certainly would NOT. Don't doubt for a moment that we won't see them again. Listen with your heart ....... He'll tell you.
Our son also died unexpectedly. Our little dog was given to us by him and his wife as they were moving and couldn't have a dog on campus. We reluctantly agreed to keep him. What joy he brought to our lives and what unspeakable comfort he gave us through some very dark days. We named him Mouse because he was so tiny. He died two years ago. We have since bought another dog, though Mouse can never be replaced, God has brighten our lives with a new furry little life, perhaps you might want to think of doing the same.
Soon and very soon, everything will be perfect!!!!