The two-year-old Palestinian Habiba Al-Askars suffers from a rare illness that disconnect the blood supply to her limbs.
Doctors who treat her have said she should be evacuated to the hospital outside the gas to save her life and some limbs.
Jordan tried to obtain Israeli permission to evacuate her for almost ten days.
A special BBC Fergal Keane correspondent traveled with Habiba and her mom at the final stage of traveling to Jordan after Israel approved his evacuation.