Is it permissible for me to pray the Fajr prayer a little late?

Intentionally delaying Fajr prayer until after sunrise is considered a major sin. As for delaying it before sunrise, this is contrary to the Sunnah (definition), as the hadiths indicate that the Prophet (peace and blessings of Allah be upon him) used to pray it in ghalas (at the very beginning of its time). The Fajr prayer is considered performed on time if it is offered before sunrise. As for sleeping through it or forgetting it, there is no sin in these cases, but it must be made up immediately upon waking up or remembering, while also taking measures to ensure one wakes up.