The Mary Plain books are by Gwynedd Rees, I think, and were about a bear, a real one from the bear pits in Berne, who went to live with humans. I think they may be out of print now.
Pity she doesn't like teddies. Otherwise she might have liked The Shoe Shop Bears by Margaret J Baker.
If it's rabbits she loves, how about:
The Velveteen Rabbit by Margery Williams Bianco;
There and Back Again by Harold Jones;
Lollopy by Susan Dunbar and Joyce Varley.
The last two are out of print but do turn up on secondhand book sites.
As she likes doll stories perhaps she would like the Five Dolls in a House series by Helen Clare. Again, out of print but it does turn up secondhand. I loved it at her age and so did my daughter.
Other doll stories she might like include a few more Rumer Goddens, namely Little Plum, The Fairy Doll, Candy Floss, Impunity Jane, and The Story of Holly and Ivy.
And there's also Sally Gardner's The Countess's Calamity, and Boolar's Big Day Out.
On the general front, what about the first three Little House books by Laura Ingalls Wilder.
And Mardie's Adventures by Astrid Lindgren, and Josephine, and Hugo and Josephine by Maria Gripe. Out of print but worth looking for.
I have gone on a bit but we are book mad in this household.