Praise be to Allah.
If a woman dies with a child in her womb, or she dies during childbirth or after childbirth but within the period of nifaas (post-partum bleeding), she is considered to be a shaheedah in sha Allaah. Raashid ibn Hubaysh narrated that the Messenger of Allaah (peace and blessings of Allaah be upon him) entered upon ‘Ubaadah ibn al-Saamit when he was sick and said, “Do you know who is a shaheed (martyr) in my ummah?”The people remained silent, then ‘Ubaadah said, “Help me to sit up.” They helped him to sit up, then he said, “O Messenger of Allaah, (is it) the patient one who seeks reward from Allaah for his patience?” The Messenger of Allaah (peace and blessings of Allaah be upon him) said, “Then the martyrs among my ummah would be very few. Being killed for the sake of Allaah is martyrdom, the plague is martyrdom, drowning is martyrdom, stomach disease is martyrdom, and if a woman dies during the post-partum period, her child will drag her to Paradise by his umbilical cord.” The umbilical cord is that which is cut by the midwife when the child is born. The hadeeth was narrated by Imaam Ahmad in his Musnad with a saheeh isnaad. (al-Musnad, 3/489). There is a corroborating report narrated by Maalik (1/233) and Abu Dawood, 3/482).
‘Ubaadah ibn al-Saamit also narrated that the Messenger of Allaah (peace and blessings of Allaah be upon him) said, “Who is counted as a shaheed among you?” They said, “The one who fights and is killed for the sake of Allaah.” The Messenger (peace and blessings of Allaah be upon him) said: “Then the shaheeds among my ummah would be few. The one who is killed for the sake of Allaah is a shaheed; the one who dies of plague is a shaheed; the one who dies of a stomach disease is a shaheed; the woman who dies with a child in her womb is a shaheed.” This was narrated by Imaam Ahmad, 5/315, and by Ibn Maajah, and by Ibn Hibbaan in his Saheeh, who said its isnaad is saheeh. A report with a similar meaning was narrated by Muslim, as referred to above.
With regard to how you should take care of your daughter after her mother’s death, this means that you should spend on her, clothe her, teach her good manners and educate her, etc. This is obligatory upon you, and you will have the reward for that as long as your intention is sincerely for Allaah. But this is not counted as sponsoring an orphan, because according to sharee’ah the orphan is the person whose father dies whilst he or she is still a child. Muslim reported in his Saheeh that Abu Hurayrah (may Allaah be pleased with him) said: the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The one who sponsors an orphan, whether he belongs to him or to someone else, and I will be like these two in Paradise” – and Maalik made a gesture with his forefinger and middle finger. What is meant by “who belongs to him” is that the sponsor is related to the orphan, e.g. his grandfather, mother, grandmother, brother, sister, paternal uncle, paternal aunt, maternal uncle, maternal aunt, or other relative. What is meant by “or to someone else” is that the sponsor is a “stranger” (i.e., not closely related) to the orphan. Your duty towards your daughter is to spend on her food, drink, clothing and shelter, and take care of her Islamic upbringing, teaching her about her religion and instilling the pure Islamic ‘aqeedah in her heart.