What does this hadith mean: ʻAa'ishah, may Allaah be pleased with her, narrated that she used to play with dolls in the presence of the Prophet, sallallaahu ʻalayhi wa sallam, and that her friends also used to play with her. When the Prophet, sallallaahu ʻalayhi wa sallam, would enter (her dwelling place), they used to hide, but the Prophet, sallallaahu ʻalayhi wa sallam, would call them to join and play with her. (Playing with dolls and similar images is forbidden, but it was allowed for ʻAa'ishah, may Allaah be pleased with her, at that time as she was a little girl who had not yet reached the age of puberty.) (Fath Al-Bari, page 143, Vol.13)

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

This hadeeth underlines the thoughtfulness of the Prophet, sallallaahu ʻalayhi wa sallam, towards ʻAa'ishah and her young age as he used to invite young girls to play with her and gave her permission to play with dolls, although they are images of living beings. Ibn Battaal commented on this hadeeth, saying, “The hadeeth indicates that the toys that young girls play with are allowed, meaning dolls, which are essentially statues. We do not find an interpretation for this concession except that it is granted to young children for playing with.” [Sharh Saheeh Al-Bukhari] When the Prophet, sallallaahu ʻalayhi wa sallam, entered the house while these young girls were playing with ʻAa'ishah, they would hide behind the curtains out of shyness.

The statement that you attributed to Ibn Hajar was actually cited by Ibn Hajar on the authority of Al-Khattaabi . Ibn Hajar quoted the statement of Al-Khattabi and underlined his reservation on the view suggesting that ʻAa'ishah had not reached the age of puberty then. He concluded that his view was more preponderant. He wrote:

“Al-Khattabi commented on this hadeeth, saying, ‘It is deduced from this hadeeth that playing with dolls is not like the amusement with other images concerning which the threat of punishment is mentioned. Rather, it was deemed permissible for ʻAa'ishah to play with these dolls because she had not yet reached puberty then.’ I say: to say with certainty that she had not yet reached the age of puberty is questionable, though it might possibly be so. This is because ʻAa'ishah was fourteen years old at the time of the Battle of Khaybar - either exactly fourteen years old, or having just passed her fourteenth year, or approaching it. As for her age at the time of the Battle of Tabook - she had definitely reached the age of puberty by then. Therefore, the strongest view is that of those who said that it was in Khaybar (i.e. when she had not yet reached the age of puberty) and made reconciliation between the apparently contradictory rulings on the permissibility of dolls, in particular, and the prohibition of images, in general, as Al-Khattaabi said (i.e. images are prohibited, except in the case of dolls for young girls). To reconcile texts is better than to assume that they are contradictory.”

Allaah knows best.