Should he offer ‘aqeeqah for a baby who died immediately after birth?

It is prescribed to offer ‘aqeeqah for her, because of the general meaning of the evidence concerning that, which includes the following: 

1 – It was narrated from Salmaan ibn ‘Aamir (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “Every child should have his ‘aqeeqah, so shed blood for him and wipe the dirt away from him.” Narrated by al-Tirmidhi, 1515; al-Nasaa’i, 4214; classed as saheeh by Shaykh al-Albaani (may Allaah have mercy on him) in al-Irwa’, 4/396. 

2 – It was narrated that Samurah ibn Jundub (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Every child is in pledge for his ‘aqeeqah, so slaughter (the sheep) for him on the seventh day, and give him his name, and shave his head.” Narrated by al-Tirmidhi, 1522; al-Nasaa’i, 4220; Abu Dawood, 2838. classed as saheeh by al-Albaani (may Allaah have mercy on him) in al-Irwa’, 4/375. 

If it is not appropriate to invite people to gather for the ‘aqeeqah meal because the infant has died, then you can give some in charity, eat some and give some as gifts.