Isaac, vice-president of the advocacy group Road of Success, said: "The Isis foreign fighters were at her door and they told her 'you have two choices, you are to leave now or you are to pay the jizya'.
"She said 'I will pay, give me a few seconds my daughter is in the shower'.
"They said 'you don't have a few seconds' and they lit the house with a torch from the bathroom the daughter was showering in."
Isaac was speaking during a conference in New York on Christians experience and persecution last month.
Despite escaping the burning home, the girl died as a result of her injuries in hospital and in her mother's arms, where she urged her to forgive the militants, Isaac said, reported the Express.
"The daughter had four degree burns and the mother took her daughter, scrambling, doing anything to save her.
"Rushed her to the hospital and her daughter died in her arms. The last thing her daughter said: 'Forgive them.'
"In the midst of darkness there is light. When there is light there is hope," she added.
In January 2014, Isis captured the Syrian town of Raqqa and made it its de facto capital city. In June 2014, the group shocked the world when it seized Mosul, Iraq's second largest city.
During their capture of territory, thousands of Christians were forced to flee in a country that one Christian charity said was "one of the most difficult places in the world to be a Christian".
An Open Doors spokesman added in comments to the Express: "Sadly this is just one more example of the atrocities being committed by extremists in this region, but I regularly hear of incredible stories of faith like this where Christians forgive their persecutors."