Beth,
I hate to put a damper on your enthusiasm but, find out what breed it is and then check with a vet. I have a neighbor that had to get her dogs stomachs operated on because it always chewed on stuffed toys. They found out that the stuffing never exited the dogs body and eventually cost them close to $2000!!! And they almost lost their pet. I had a quilt for my animals and never had any problems, a few chews but they ever consumed vast amounts. I used cotton batting and that was back in the day when there was no scrim of any kind to keep it together, so it probably could get digested,, an option to true batting would be top, back, and a piece of flannel fabric for the batting. It would be all cloth and they'd be able to see if the puppy is just chewing or actually tearing chunks and swallowing. Their dog was a 'spuds mckenzie', I do t know the proper bread name though.
I wonder if you used heavy weight, outdoor type upholstery fabric and they could get wood shavings to fill it with if you put a zipper on an end. The puppy would have a comfy bed that could sleep on.
Just a thought,
Luann