Praise be to Allah.
The father is like the shepherd of his household and is responsible for his flock, as the Prophet (peace and blessings of Allaah be upon him) said. Based on that, he should educate his children and teach them to fulfil obligations and avoid haram (unlawful) things. That includes telling them to pray when they reach the age of seven years, because of the report narrated by Abu Dawood (495) from ‘Amr ibn Shu’ayb, from his father, from his grandfather, who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Tell your children to pray when they are seven years old and smack them (lightly) if they do not pray when they are ten, and separate them in their beds.” Classed as saheeh (authentic) by al-Albaani in Saheeh Abi Dawood.
But the father should be kind in teaching his small children how to pray, and he should encourage them by praising them, and giving them gifts and rewards so that they will get used to it and love it.
You can delay waking your daughter up until near sunrise, and encourage her to sleep early so that it will be easier for her to get up.
There is nothing wrong with you not waking her up on days when you think it will be too hard for her to wake up, because – for example – she went to sleep late or because it is very cold, and so on.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: I have a son who is about nine years old; should I wake him up for Fajr prayer?
He replied: Yes, if a man has children, male or female, who have reached the age of ten, he should wake them up. With regard to children who are younger than that, if he wakes them up so that they may pray on time, that is better, but there is no sin on him if he does not do that. But it is better to wake them up, because the Prophet (peace and blessings of Allaah be upon him) said: “Tell your children to pray when they are seven years old and smack them (lightly) if they do not pray when they are ten, and separate them in their beds.” End quote from Fataawa Noor ‘ala’l-Darb.
He was also asked: My son is eight years old; should I wake him up to pray Fajr? If he does not pray, am I sinning?
He replied: It seems that it depends. If it is winter, for example, and it is very cold, then there is nothing wrong with leaving him and telling him to pray when he wakes up. But if the weather is normal and there is no harm done by waking him up, then you should wake him up so that he will get used to praying with the people. Nowadays, praise be to Allaah, there are young boys between the ages of seven and ten whom we see coming with their fathers to pray Fajr. If a child gets used to that from an early age there is a great deal of goodness in that. But if it causes hardship, then you do not have to wake them up. But when they wake up you should tell them to pray. End quote from al-Liqa’ al-Shahri (40/18).
And Allaah knows best.