This story comes from Dora Diamant, although OPs version is Max Brod's retelling of it, which has some differences.

Interestingly, there is another story about a doll, this one from a letter of Kafka to his sister Elli:

Recently I had an amorous escapade. I was sitting in the sun in the Botanical Garden . . . when the children from a girls’ school walked by. One of the girls was a lovely long-legged blonde, boyish, who gave me a coquettish smile, turning up the corners of her little mouth and calling out something to me. Naturally I smiled back at her in an overly friendly manner, and continued to do so when she and her girlfriends kept turning back in my direction. Until I began to realize what she had actually said to me. “Jew” is what she had said.