Is it permissible to be an hour late for work so that one's arrival coincides with the doctor's appointment, knowing that the work is dependent on one's presence?

It is not permissible to be late for official working hours or to leave before they end without an excuse, because it involves a breach of contract. Allah Almighty said: "O you who have believed, fulfill [your] contracts," and the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions in what is lawful." The fact that a doctor arrives late does not justify your lateness, for your time is owned by your employer.