Short answer
Yes. Aisha said she used to play with dolls in the Prophet's ﷺ home and her friends came to play with her. The report is in Sahih al-Bukhari. Scholars cite it as proof that dolls for young girls are allowed and that she was still young at the start of her marriage.
The hadith of Aisha's dolls is authentic, and scholars take it as the basis for allowing dolls for children. Many Hanafi scholars, including Deobandi muftis, limit this to simple dolls without detailed faces, since her dolls were plain figures of cloth.
The four schools agree on this.
Explanation
Aisha said: "I used to play with dolls in the presence of the Prophet ﷺ, and I had friends who played with me." When he came in, her friends would hide out of shyness, and he would send them back to play with her. The report is in Sahih al-Bukhari, in the book of manners.
Another narration, in Sunan Abi Dawud, tells how the Prophet ﷺ returned from an expedition and saw among her toys a horse with two wings made of cloth. He asked what it was. She said a horse. He asked: a horse with two wings? She answered: have you not heard that Sulayman had horses with wings? He laughed until his back teeth showed.
The story shows the warmth and play in his home. He did not stop her play, he joined in kindly, and he made sure her friends could stay. Scholars also note that these reports agree with the narrations of her young age at the start of the marriage.
On the ruling side, scholars take this hadith as the basis for allowing dolls for children. Many Hanafi scholars, including Deobandi muftis, say her dolls were simple cloth figures, so they allow simple or faceless dolls and advise against lifelike ones; other scholars allow ordinary dolls for play. See Are dolls and toys allowed for Muslim children? Read more about Aisha on Aishah bint Abi Bakr.
The evidence
Sahih al-Bukhari 6130
Sahih... كنت ألعب بالبنات عند النبي ...
"I used to play with dolls in the presence of the Prophet."
The main report of her dolls.
Sunan Abi Dawud 4932
Graded sahih... فرس له جناحان ...
"A horse that has two wings."
The story of the winged toy horse, graded sahih.
Where the ruling is recorded
- Fath al-Bari (Ibn Hajar), Commentary on Kitab al-Adab, chapter on being cheerful with people. Discusses the dolls and why scholars made them an exception to the rule on images.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Salah, chapter on what is disliked in prayer, discussion of images. The Hanafi rules on images of living beings.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.