Is the action that led to the death of the child considered intentional killing or an error, given that she was intubated without the doctor's permission due to his negligence, and in light of the shortage of medical staff?

If a physician errs in prescribing medication or its method of administration, leading to the patient's death, the physician is liable and must offer expiation and pay blood money, unless the victim's guardians pardon the blood money. This applies to an ignorant physician who practices medicine without knowledge, and to a skilled physician if he errs in prescribing medication, leading to organ damage or death, or if he exceeds accepted limits or falls short in diagnosis. The reference for determining liability is the judgment of three trustworthy physicians. If they confirm the correctness of his action, then nothing is incumbent upon the physician. But if they confirm his error and that it was the cause of death, then expiation (fasting for two consecutive months) is incumbent upon the physician, and the blood money is paid by the 'Aqilah (male relatives on the father's side). If the 'Aqilah does not exist, or refuses, or is unable to pay, the blood money is waived according to some scholars. The physician must also repent, strive to learn, exercise caution in decision-making, and continue his work.