Children's fiction, rabbit hit by car, animal heaven

My usual approaches have been useless here. I read this book as a child, so it couldn't have been published after 1995 or so. I don't remember if it was a picture book or a chapter book, but I'm pretty sure the cover had a big picture of a rabbit with a giant full moon in the background.

This story had two parts. First, a rabbit, probably a jackrabbit, is hopping around in the forest when it comes by a road. A car is coming, which it has never seen before. At first it thinks the car is a predator, but gets curious when the car doesn't hurt it, so it runs alongside the car and races it. It ends up getting hit by the car and being killed. Some schoolchildren find the rabbit's body and it makes them sad, and they get an idea to write a story about the rabbit.

For the second part, we're back with the now-dead rabbit who gets to choose which heaven he wants to go to. He could go to regular animal heaven, but because the children wrote a story about him, he's now a fictional character and could choose to go to a special heaven for fictional creatures such as the Velveteen Rabbit, etc.

Thanks in advance for your help!

Bump.

Any ideas?

Someone on Goodreads found it. It was called Hare's Choice by Dennis Hamley.

Thanks! I'll keep an eye out for it.