Please relax. This isn’t a problem. It’s her solution for not having the playmate she wants. It is unlikely to cause her anxiety in the future. If anything, it’s probably relieving it.
It’s very common for children to develop this kind of attachment to a stuffed animal or to imaginary playmates, especially if they don’t have the friends or family they want. Kids who create the kind of play you describe are usually exceptionally smart and creative. Accept the bear. Get into it with her. Talk to Chubbie. Set a place at the table and make sure to ask your daughter questions about him now and then. Most kids are delighted when the grown ups decide to play.
Meanwhile, your daughter is longing for a sibling. You may not be able to answer that wish, but you can certainly include more children in her life. Quality time with you doesn’t answer that need. Set up play dates. When she is a little older, arrange for sleepovers. Take one of her friends along when you go to the park or do something special. Once she discovers that she can have playmates, she’ll be less intense about wanting a brother or sister.
At some point, you might explain to her that some families are big and some are small; that you are meant to have one special child and that you are so glad it is her.
I wish you well.