Special Request: Book Identification

I especially love the dogs.
I’ve got a different sort of request today, from a reader trying to find a story he remembered from his childhood that he hasn’t been able to identify. I’m hoping it’s familiar enough to someone out there on the Interwebz to give it a name and an author for him.
Read on for his description:
It was a story about a little girl who was somehow transported to a parallel universe. Where she landed was near a large glade-like area. There were a lot of cute forest animals grazing and sleeping there: rabbits, squirrels, baby deer, etc. One of the rabbits looked up and saw her. It gave some kind of signal and all of the animals started looking at her. Suddenly they all seemed to look angry and began snarling and baring their fanged teeth. They began coming toward her. She was afraid and began to run. They chased her, making the most horrible noises she ever heard. Just when she was sure they would overtake her, she heard something yelling at her. “Over here! Hurry!”. She looked and it was an alligator with wings. She got scared again and almost stopped running. “Don’t stop. Get over here and jump on my back. It’s the only way I can save you”. She looked back and saw the horde of animals was much closer. She ran over to the alligator who lowered itself to let her get on. “Hold on!” it yelled. He began running and suddenly he left the ground as his wings unfolded. They soared up just beyond the lunges of the frenzied animals and flew away.
If you’re getting some Wizard of Oz vibes from this, you’re not alone. A lot of stories of that book’s era told tales with young children as protagonists in fantasy settings, but it’s not from Baum’s work as far as we can tell. You are certainly welcome (even encouraged) to correct me on that.
If this seems at all familiar to any of you, please reply and help out.
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