Exactly. My Parents went for Hajj back in 2000 via Cairo (Frakfurt-Cairo-Jeddah). Since the Egypt Air flight was a special Hajj Flight they were told at the Cairo Airport to get into Ihram as Jeddah is within the Ihram boundaries.
So better get into Ihram when u r in Dubai. As far as i know there is “Marhaba Service” in Dubai which can help u prepare for Umrah and Hajj. If u r flying with Emirates they’ll surely help.
May Allah SWT be with u.